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Locally resonant metamaterials have recently emerged and gained attention in the field of noise control engineering. The addition of resonant structures to a flexible partition on a sub-wavelength scale enables a targeted frequency range of strongly reduced vibration and sound transmission. These structures have been widely studied and are typically analyzed using infinite periodic structure theory. The implications of nonsub-wavelength resonator spacing on the sound transmission loss of metamaterial partitions as well as on the representativeness of the infinite periodic structure modeling are, however, less well known. In this technical brief, it is shown that, although a shifted sound transmission loss peak can be predicted for partitions with nonsub-wavelength resonator spacing when using infinite periodic structure modeling, the sound transmission loss enhancement is not guaranteed for their finite structure counterparts.

The sound velocity in ice is of great significance to the acoustic propagation characteristics of ocean channels under ice cover and the acoustic characteristics of underwater targets. Freshwater ice has a uniform crystal structure under normal conditions. The freezing process of sea ice is more complicated compared to fresh water ice. The sea ice contains a lot of bubbles, brine, solid particles and other impurities. Due to the large difference in the structure and composition of ice in different states, it is very different from the common sound transmission media in the past. Therefore, in order to accurately describe the acoustic propagation characteristics of the ocean channel under the ice cover, it is necessary to measure the longitudinal sound velocity in the ice accurately. A direct method for measuring the speed of longitudinal waves in ice is studied in this paper. The propagation time of high-frequency pulses in the ice is used in this research to determine the speed of longitudinal waves. For the same piece of ice, the method of averaging multiple measurements was used to reduce the measurement error. Six tests were performed on typical ice with different structural characteristics. The six tests were the fresh water in Songhua Lake area of Jilin Province in 2019, the high mud content sea ice in the coastal area of Bohai Bay in 2020, the low mud content sea ice in Liaodong Bay area in 2021, the artificial quick-frozen sea ice and fresh water ice at -20°C, and the summer Arctic sea ice obtained in the eleventh Arctic scientific survey in 2020. The sound velocity of longitudinal waves in ice was measured at 12kHz, 25kHz, 50kHz, 75kHz, and 100kHz. The acoustic properties of ice are determined by its own state. The measurement results have certain fluctuations, because the test results were closely related to the sample test environment and test process. The measurement results of longitudinal wave sound velocity were described by the measurement mean value and standard deviation in order to scientifically express the longitudinal wave sound velocity in ice. The test results showed that the longitudinal sound velocity in high mud content sea ice was about 3360±162m/s, 3270±78m/s in low mud content sea ice, 3769±54m/s in artificial sea ice, 3772±57m/s in lake ice, 3729±23m/s in artificial fresh water ice, and 3893±86m/s in Arctic ice. Under the same measured temperature, the compression wave sound velocities in most ice media are stable at 3750 m/s. The research methods and results in this paper provide references for related research on the acoustic properties of ice media, the acoustic propagation characteristics under ice cover and target acoustic characteristics in ice area.

Heating ventilating and air-conditioning systems which equip our buildings/rooms represent noise sources unfavorable affecting the people decent living and working conditions. Usually, silencers are used to reduce the annoying sound from these systems. They are lined with different materials and they have various geometries in order to satisfy the consumer needs, in terms of acoustic comfort. Sound absorption and sound transmission loss characterize the materials acoustic properties, but it is not mandatory that a good absorbent material to be also an efficient one from transmission loss (attenuation) point of view. Our paper is focused on an acoustic study of different materials lining three commercial silencers of same geometry and size. We have recorded the sound data according to standards: ISO 10534-1:1998 for the sound absorption coefficient and ISO 7235:2009 for the transmission loss rating. Third octave analysis with LabView soft is used to process the sound information and then the two parameters values are calculated. The acoustic characteristics of the tested materials are discussed and features that recommend them to be used as lining materials for silencers are highlighted.

The acoustic performance of glass fiber felts after water absorption was researched in the paper. The effects of sound frequency and moisture content on the sound transmission loss (STL) and sound ...

In order to improve the sound emission in a structure that is made out of fiber reinforced plastics, the structure-borne sound propagation is selectively manipulated by a local or global modification of the fiber-matrix bonding. This manipulation is induced by a reduction of the fiber-matrix bonding by using a hydrophobic and therefore non-polar surface treatment of the dry fiber. The content of this paper is to present the preliminary investigations regarding the effectiveness of test specimens with two different hydrophobic plasma treatments compared to a reference without any modification. To this end, several tests were performed in order to prove the effectiveness of the respective modification to the fiber-matrix bonding. The specimens are composite laminated plates with a uni-directional lay-up. The materials which is used for the composite laminate is carbon fiber in combination with an epoxy matrix. Positive results are demonstrated regarding the feasibility to apply a hydrophobic plasma coating on a dry NCF (non-crimp-fabric) with sharp and defined edges. Since the determination of the loss factor and storage modulus according to the standard DIN EN ISO 6721-3 (Procedure B) did not show any relevant changes in comparison to the reference, a simplified test according to the standard DIN EN ISO 6721-3 (Procedure A) was performed in order to check if a suitable test environment was chosen. The results showed a measurable growth of the loss factor up to 71% in comparison to the reference.

Acoustic micro-membranes (AMMs) have theoretical advantages in terms of light weight yet high sound transmission loss (STL) at low frequency, but an actual medium- or large-scale specimen usually shows a significant performance degradation. Those lumped-parameter models developed so far lose their accuracy on theoretically describing the actual sound transmission loss of such an assembly. In this paper, the influence of the frame vibration is explored, and an acoustic theory based on a distributed parameter system is established. By coupling the vibration of the frame and the membranes, this theory shows how the acoustic impedance of the assembly depends on the number of membrane cells and the dimensions of the membranes and frame. As the assembly becomes larger, its global response is no longer dominated by the membrane but by the frame, while the latter determines the upper limit of the STL of the whole assembly. Compared to the well-developed lumped-parameter model that works only for small-scale AMMs, this work provides a theoretical foundation for designing larger size yet high loss AMMs, and may pave the way for their use in noise control engineering.

Acoustics represents a quality feature of a passenger vehicle. During the first development phases, prediction tools of the acoustic performance are required to assess in the design process. A combination of numerical and experimental data provides a good compromise between accuracy and modeling effort. A key part of the airborne noise transmission chain are the different passive acoustic treatments applied to minimize the noise impact. These treatments usually include one or more layers of poroelastic media. They exhibit a highly dissipative behavior, making them suitable as noise barriers but, at the same time, complex to model. This article aims to identify the parameters that define the appropriate numerical modeling approach for vibroacoustic systems with poroelastic acoustic packages. Two different concepts for the noise reduction based on poroelastic materials have been investigated, namely the insulation through a spring–mass component and the absorption of a porous layer. The essential principles of the theory of poroelasticity are recalled and three material formulations are derived. The application range of each material model is examined with the help of two configurations: a flat plate and a simplified model of a vehicle front end. The acoustic response of the system is solved with the help of the finite element method using the different material formulations for the description of the poroelastic layers, and the results are compared to measurements conducted in a window test bench. Finally, the main findings are summarized and recommendations towards a more realistic representation of the complete transmission chain are presented.

Purpose With the development of the modern technology and aerospace industry, the noise pollution is remarkably affecting people’s daily life and has been become a serious issue. Therefore, it is the most important task to develop efficient sound attenuation barriers, especially for the low-frequency audible range. However, low-frequency sound attenuation is usually difficult to achieve for the constraints of the conventional mass-density law of sound transmission. The traditional acoustic materials are reasonably effective at high frequency range. This paper aims to discuss this issue. Design/methodology/approach Membrane-type local resonant acoustic metamaterial is an ideal low-frequency sound insulation material for its structure is simple and lightweight. In this paper, the finite element method is used to study the low-frequency sound insulation performances of the coupled-membrane type acoustic metamaterial (CMAM). It consists of two identical tensioned circular membranes with fixed boundary. The upper membrane is decorated by a rigid platelet attached to the center. The sublayer membrane is attached with two weights, a central rigid platelet and a concentric ring with inner radius e. The influences of the distribution and number of the attached mass, also asymmetric structure on the acoustic attenuation characteristics of the CMAM, are discussed. Findings In this paper, the acoustic performance of asymmetric coupled-membrane metamaterial structure is discussed. The influences of mass number, the symmetric and asymmetry structure on the sound insulation performance are analyzed. It is shown that increasing the number of mass attached on membrane, structure exhibits low-frequency and multi-frequency acoustic insulation phenomenon. Compared with the symmetrical structure, asymmetric structure shows the characteristics of lightweight and multi-frequency sound insulation, and the sound insulation performance can be tuned by adjusting the distribution mode and location of mass blocks. Originality/value Membrane-type local resonant acoustic metamaterial is an ideal low-frequency sound insulation material for its structure is simple and lightweight. How to effectively broaden the acoustic attenuation band at low frequency is still a problem. But most of researchers focus on symmetric structures. In this study, the asymmetric coupled-membrane acoustic metamaterial structure is examined. It is demonstrated that the asymmetric structure has better sound insulation performances than symmetric structure.

This paper explores further possibilities of structurally-efficient honeycomb sandwich panels by replacing one of the faceplates with the perforated faceplate from the viewpoint of sound absorption coefficient (SAC) as well as sound transmission loss (STL). An analytical model is presented to calculate both the STL and SAC, with the displacements of the two faceplates assumed identical at frequencies below the faceplate resonance frequency. Influences of core configuration are investigated by comparing different honeycomb core designs. Finite element (FE) models are subsequently developed to validate the proposed analytical model, with agreement achieved. Subsequently, parametric surveys, including the influences of perforation ratio, pore size and core configuration on STL and SAC, are conducted based on the analytical model. Unlike classical honeycomb sandwich panels which are poor sound absorbers, honeycomb sandwiches with perforated faceplates lead to high SAC at low frequencies, which in turn brings about increment in the low frequency STL. Moreover, sandwich panels with triangular cores are found to have the lowest peak frequency in the STL and SAC curves compared with the other kinds of sandwich panels having the same effective mass and perforations.

This paper analytically addresses the sound transmission loss (STL) performance of finite triple-wall sandwich panels lined with poroelastic materials and clamp mounted on an infinite rigid baffle in the presence of an external mean flow. The wave propagation in poroelastic media is addressed using Biot's theory. The coupling methods between the poroelastic core and facing plates are associated with different boundary conditions and various panel configurations. The Galerkin method and the modal superposition theory are used to deal with the clamped boundary conditions and finite extensions as well as to transfer the integral function to a matrix equation. The analytical model is verified by comparing to previous results of infinite triple-wall sandwich panels and finite triple-wall panels without poroleastic materials. The numerical results show that the triple-wall panels have superior STL to their double-wall counterparts due to the existence of an additional partition. The finite dimensions of the triple-wall sandwich panels with clamped boundary strongly influence the STL at low frequencies, and this effect is coupled with that of the external mean flow. The air layer plays a critical role in the sound insulation properties that vary among different panel configurations, and the configurations with two air layers exhibit the optimal overall sound insulation performance.

In this paper, a modelling approach is developed for predicting the vibroacoustic response of infinite, plane, 1- or 2-dimensionally periodic structures, including the forced response, sound transmission and radiation. This method combines a wave and finite element method with a space-harmonic assumption. A periodic cell of the structure is modelled using a conventional finite element method to find the mass and stiffness matrices. Wave propagation in the fluids is modelled analytically. The response at the interface between structure and fluid is represented in terms of a series of space harmonics. The effects of the fluids on the structure are modelled as a series of equivalent nodal forces. By post-processing the mass and stiffness matrices along with the applied forces using periodicity theory and equilibrium conditions, a spectral dynamic stiffness matrix is derived to calculate the response to a convected harmonic pressure. Excitation of the structure by oblique plane waves and a diffuse sound field are considered, together with the consequent sound transmission. The response to general excitation and the consequent radiation are also determined. For complex structures, model reduction using component mode synthesis is suggested. Various numerical examples are presented to illustrate this method. For simple structures, analytical solutions are available for comparison with the predictions made using the proposed method. For complicated structures, vibroacoustic analysis using analytical methods is difficult. However, the method developed in this paper provides a straightforward and efficient approach for estimating the vibroacoustic response of general plane periodic structures.

Membrane- and plate-type acoustic metamaterials are thin membranes or plates consisting of periodic unit cells with small added masses. It has been shown in numerous studies, that these metamaterials exhibit tunable anti-resonances with transmission loss values much higher than the corresponding mass-law. However, in most studies it is assumed that the unit cell edges (or grid) of the metamaterial are fixed. This idealised boundary condition is not applicable to real world applications in noise control. Therefore, the acoustic performance of these metamaterials under more realistic circumstances, where the grid structure cannot be perfectly rigid, can be expected to be different. In this contribution, the vibro-acoustic behavior of membrane- and plate-type acoustic metamaterials with a non-rigid grid is investigated. For this purpose, an efficient analytical model is developed to predict the eigenmodes and sound transmission loss of such metamaterials. In this model, elastic unit cell edges are modelled using a grid of Euler-Bernoulli beams and the sound transmission loss can be calculated for oblique incidence. A comparison to FEM simulations shows that the proposed model yields the same results but with a considerably reduced computational effort. The analytical model is then used to discuss the vibro-acoustic properties of the metamaterial, with particular focus on the influence of the mass and stiffness of the grid beams. It is shown that even when a non-rigid grid and diffuse incident sound fields are considered, the transmission loss of the metamaterial exhibits anti-resonances with remarkably high noise reduction values. These anti-resonances can be tuned by choosing appropriate values of the grid parameters. Furthermore, the formation of band gaps in the propagation of bending waves is discussed by investigating the dispersion curves of the metamaterial. The results in this contribution show that membrane- and plate-type acoustic metamaterials can still efficiently reduce low-frequency noise, even when the unit cell edges are not assumed to be fixed. This important finding and the proposed analytical modal can support the utilization of these metamaterials in practical noise control applications.

Vibroacoustic performance of the doubly curved thick shell is explored based on the three dimensional sound propagation approach as well as state space solution. In fact, the main aim is particularly focused on inspecting the influence of using three-dimensional theory through sound transmission loss (STL) of the structure which includes more reliable and accurate results especially for relatively thick and thick shells even in high frequency domain in comparison with other theories. In order to achieve this end, firstly stress and strain components are developed to present the governing equations of thick shell. This procedure is carried out by dividing the shell into s layers. Then, a solution technique is provided on the basis of state vector methodology wherein approximate layer model along with local transfer matrix are performed. Moreover, this method is followed by global transfer matrix method for the all layers of structure. As an outcome, in results section, not only the accuracy of the offered results is proved but also the importance of employing the current theory in high frequencies is revealed. Another remarkable achievement of this work is related to nominate the dip points of STL diagram. On contrary to panels, doubly curved shells contain two dips, because of their both radii of curvatures. In this work, the first dip is nominated as curvature frequency. The second dip is similar to that of panels at high frequency zone. Thus, it is called as coincidence frequency. Finally, the behavior of the transmitted pressure and the effect of curvatures on the position of curvature frequency are discussed.

Acoustic conditions in a symphony orchestra on a concert hall stage are very different from those on an empty stage. Since inter-orchestral sound transmission and other acoustic conditions with the orchestra present is easier to simulate than to measure, a method for simulations in Odeon models of orchestras in different rooms was developed by this author. This method was applied in the Grieghallen Renewal Project, which involved changes in concert hall, orchestra pit, and rehearsal hall. The resident orchestra members gave their overall rating of playing conditions in the home venues in addition to a number of international venues. Acoustical conditions in the rated venues were simulated and compared with ratings. Several metrics were investigated, and their correlation with subjective ratings varied between r2 = 0.09 and r2 = 0.85. It turned out the orchestra clearly preferred to play in conditions where the direct component and the reverberant component of the inter-orchestral sound-transmission on average were equally strong, D-R| = 0. Any deviation from equality was associated with reduced preference, with correlation coefficient r = &minus, 0.92. Several interesting implications and interpretations of the result are discussed in the paper.

According to the third-order shear deformation assumption, this paper analytically investigates the sound transmission loss (STL) through a rigidly baffled finite rectangular double wall piezoelectric plate structure made of functionally graded materials (FGMs) with enclosed acoustic cavity, under harmonic plane sound excitation and initial external electric voltage. The effective piezoelectric material properties of each plate are supposed to be continuously variable across the thickness direction using a power law model in terms of the volume fractions of the material phases. The coupled vibroacoustic governing equations are achieved utilizing Hamilton’s principle and then solved analytically by applying the sound velocity potential method in conjunction with double Fourier series expansions to determine STL equation. Numerical studies are performed to illustrate the effects of the acoustic cavity depth, initial external electric voltage, incident elevation angle, gas type used in acoustic cavity, and material gradient on the changes of STL curves of simply supported double wall FGM piezoelectric plate. The profound effect of these factors on sound isolation performance is clearly shown.

Considering the impact noise as a major social issue in many countries, extensive work have been developed aimed at reducing the noise level in dwellings. Laboratory tests were carried out to investigate the acoustic performance of same constructive proposals, arranged to reduce the impact sound transmission. According to this study, acoustic performance of both types of floors differs significantly, with a difference of up to four times that of the effect of floating floor system on a homogeneous floor in some cases. The conclusions can help to determine the proposal of best suitable constructive solutions in accordance with legal regulations.

Finite structures play a more realistic role in applications designed for sound and vibration isolation. Doublepanel structure with poroelastic cores is able to exhibit a superior sound insulation performance in mid-high frequency range, while is relatively inferior to isolate waves at low frequencies. In order to further reduce sound transmission at low frequencies and cater for the actual situation, this paper decides to introduce the metamaterial concept into finite double-wall sandwich plates and presents an analytical model to calculate the sound transmission loss through the metamaterial-based double-panel with fully clamped boundary conditions. The metamaterial-based double-wall sandwich plates are constructed by replacing the bare panel with the metamaterial plate, consisting of a homogeneous plate and periodically attached local resonators. Biot's theory is used to examine the wave propagation in the poroelastic medium. The vibro-acoustic problem of the proposed sandwich plate is solved by employing the modal superposition theory and the Galerkin method. Numerical results show that the sound transmission is significantly reduced at low frequencies. Unique phenomena caused by attached local resonators are explained and the eff ects of resonator inerter, incident angles and damping on the sound insulation properties are also studied.

In the present study, the sound transmission loss (STL) of ultrafine glass fiber felts in terms of areal density and sound frequency has been modeled by artificial neural network (ANN), the Law of Theoretic Mass and fitting polynomial, respectively. The STL of ultrafine glass fiber felts with the areal density ranging from 0 to 300 g/m2 and at the sound frequency ranging from 500 to 6300 Hz was employed as training data for ANN. By the optimization of ANN structure, the number of neurons in the two hidden layers was determined to 8 and 4 respectively. The mean squared error of the ANN model was only 0.191 and the correlation coefficient was 0.9989, which showed high accuracy for estimating the STL of the felts. Compared with other two models, the ANN model showed excellent agreement with the measured results and it's very appropriate for the estimation of acoustic properties of ultrafine glass fiber felts.

This paper presents a theoretical model that allows to calculate the acoustic transmission loss through laminated composite pyramidal sandwich structure consisting of two parallel plates connected by trusses. First-order shear deformation theory is adopted to model the vibration of such a structure, accounting for in-plane motion and coupling between extension and flexure of the different components, and taking into account elastic anisotropy. The interaction between the structure and the surrounding fluid is taken into account by imposing a velocity continuity condition at the interfaces. The displacement and stress fields are calculated in Fourier domain by solving the set of boundary condition equations at the connecting points. The theoretical predictions for the acoustic transmission through the structure show satisfactory agreement with experimental results of a standing wave tube experiment on specimens that were fabricated by cutting trusses from carbon fiber reinforced composite plates and snap-fitting them to plates made of the same material. Numerical simulations are used to verify, the influence of the stacking geometry and material parameters on the acoustic transmission for different frequencies and angles of incidence. Conclusions are presented that are helpful for practical design.

The known methods of acoustical calculation in buildings not fully describe the phenomenon of sound transmission. This paper presents theoretical studies of the sound and vibration in building models, a method of statistical energy analysis (SEА), taking into account nonresonant phenomena and experimental testing of the specified parameters. The SEA-based equations are obtained for the energy balance, the solution of which allows to determine the sound energy in rooms and sound vibration in structures. The energy coupling coefficients, including those allowing for non-resonant sound transmission from adjacent acoustic subsystems, internal losses and the density of mode oscillation are calculated. The results of calculations and measurements of building model fragments, including identical and double partitions, are presented. The proposed method of calculation allows to predict the sound transmission through the partition with regard to adjacent structures.

Multi-objective vibroacoustic optimization of the double-walled doubly curved composite shells having poroelastic lining in its core in a diffuse field is performed based on Non-dominated sorting Genetic Algorithm-II. To present an analytical model on the basis of multi-objective optimization, the summation of sound transmission loss and transverse displacement along with weight of the structure are considered as two cost functions, which should be optimized in a diffuse field. In fact, the significant achievement of this work is to design an optimization algorithm to improve vibroacoustic fitness and weight of the sandwich doubly curved shells. In the first part of the paper, a general formulation is prepared to analyze the dynamic of the poroelastic composite sandwich structures. Likewise, some validation configurations are presented to confirm the accuracy of the current formulation. Consequently, an optimization algorithm is provided on the basis of considering some appropriate design variables including material and porous types as well as stacking sequences. In this regard, a batch of 19 benchmarks of porous core is investigated. Furthermore, a configuration of optimized points in the Pareto front is plotted in which the simultaneous effects of optimizing the weight and vibroacoustic fitness can be observed. As a result, a new approach is made through optimization of the transverse displacement of the structure as a function of various incidence and azimuth angles in three dimensional configurations with respect to different frequencies.

This study investigates into the sound transmission through a periodic acoustic metamaterial grating of finite size. The single-layer grating is constructed by periodically arranging sub-wavelength unit cells in a slab, as a part of a large baffle between two acoustic domains. The metamaterial unit cell consists of an open duct decorated with coiled resonators, which intends to suppress sound transmission using its acoustic stop-band. The space-coiling structure allows the metamaterial to operate at low frequency with a compact size. Analytical approach to predict the sound transmission loss (STL) of the combined baffle is developed, which is employed to study its sound attenuation under normal and oblique incidence. Results show that the unit cell geometry, the periodicity of grating elements, and the angle of incidence significantly affect the STL. The STL behavior of the acoustic grating is mainly governed by three physical effects, including the acoustic stop-band, the edge diffraction, and the destructive radiation interference behind the acoustic grating. Detailed mechanism studies for these effects are discussed using numerical examples. Experiment is conducted to validate the proposed numerical approach. This paper presents a theoretical framework to predict and study the performance of acoustic gratings comprised of metamaterial unit cells, which can be further extended to study phase tailoring acoustic metasurface.

In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the propagating and coupling parameters used in coupled-mode theory directly by utilizing the generalized eigenwave-eigenvalue problem from the Hamiltonian of the sound wave equations for the problem of a one-dimensional isolated on-channel resonance. This Hamiltonian formalization could be beneficial and could potentially model and parameterize a broad range of acoustic wave phenomena. We demonstrate how to use this theory as a basis for perturbation analysis of complex resonant scattering scenarios. In particular, we form the effective Hamiltonian and coupled-mode parameters for the study of sound resonators with background moving media. Finally, we provide a comparison between coupled-mode theory and full-wave numerical examples, which validate the Hamiltonian approach as a relevant model to compute the scattering characteristics of waves by complex resonant systems.

There is much potential for engineered wood products to be used beyond low-rise residential construction when incorporating the notion of hybrid systems like timber-concrete-composites (TCC). TCC systems are comprised of a timber element connected to a concrete slab through a shear connection. By combining the complimentary properties of timber and concrete, the performance of timber floors can be enhanced, including bending stiffness, load-bearing capacity, dynamic response, airborne sound transmission, structural fire rating, and thermal mass. A large number of T-beam TCC systems existed for decades; however, the growing availability of panel-type products in North America offers designers greater versatility in terms of structural and building physics performance. While stiffness and strength design of TCC systems is straight-forward, there is little design guidance available in terms of vibration and long-term performance. The bending, vibration and long-term performance for a range of TCC systems in several EWPs were validated on small-scale shear tests, floor panels subjected to serviceability loads for 2.5 years, and subsequent full-size bending tests. The tests confirmed that calculations according to the ?-method can predict the basic stiffness and dynamic properties of TCC floors within a reasonable degree of accuracy.

In this paper, a solution strategy based on the state vector technique is proposed to study the vibroacoustic performance of carbon nanotube (CNT)-reinforced composite doubly curved thick shells employing three-dimensional theory. For this purpose, the properties of the nanocomposite media are investigated by the rule of mixture which includes some productivity parameters. This approach considers various distributions of CNT which can be identical or functionally graded through thickness direction. Since the state vector solution is used to solve the three-dimensional equations of motion, the nanocomposites are divided into s layers for stress and strain components according to approximate layer model along with local transfer matrix. This process is followed by the global transfer matrix for all of the layers of thick shell. After obtaining the sound transmission loss of structure, various configurations are presented to validate the results. Hence, not only the precision of the formulation is confirmed but also the importance of considering the three-dimensional theory is remarked due to very reliable outcomes at high-frequency domain for CNT-reinforced composite thick shells. Furthermore, it is shown that the CNTs are able to enhance the sound insulation property of doubly curved structures. Finally, a new approach is made to present the sound pressure level of CNT doubly curved shells with respect to various CNT materials in different distributions.

In this paper, a systematic design method is proposed to improve the sound transmission loss of a cellular-type noise insulation panel, which is a thin rectangular plate with supporting frame. The unit cell of the noise insulation panel generates an anti-resonance effect at a certain frequency and yields a higher sound transmission loss than a flat plate of equivalent mass. Previous studies confirm that the mass ratio between the thin plate and the supporting frame has an important influence on the frequency at which the maximum sound transmission loss occurs. However, no design method to maximize the sound transmission loss at a target frequency has yet been reported, although this issue is very important for noise insulation of mechanical systems. In this regard, sizing optimization is performed using the thickness of the noise insulation panel as a design parameter. Hence, the optimal thickness distribution to maximize the sound transmission loss at a given target frequency is determined. To calculate the sound transmission loss, a finite element model of the noise insulation panel is constructed, considering the vibro-acoustic effect. Several numerical examples are presented to verify the proposed design method. The optimization results confirm that the designed unit cell exhibits high sound transmission loss at given frequencies of interest.

The sound transmission and insulation of aeronautical panels represents one of the major problem of the aircraft comfort. In the present work, a plate finite element with advanced higher-order kinematic field is proposed for the analysis of noise reduction passive control system in laminated structures. A novel Decline Population Swarm Optimization ( P D SO ) procedure is introduced and used to select the optimal parameters for the sound control. The present sound insulation passive control is based on Finite Elements obtained by applying the Principle of Virtual Displacements, taking into account the frequency dependence of the viscoelastic material, making use of higher-order Layer-Wise theories, and employing the Mixed Interpolated Tensorial Components (MITC) method to contrast the shear locking effect. The P D SO procedure is based on a decline demographic model and is characterized by high global search capabilities with reduced computational costs. The acoustic insulation of the panels is evaluated by computing its sound transmission factor using Rayleigh integral method. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the acoustic optimization procedure for the design of viscoelastic plates.

Traditional acoustic regulations in practice are used to have major obstacles in low frequency range, for which absorbers or suppressors have thicknesses that are comparable to their working wavelength. We present an acoustic structure-based “coiling-up space” to achieve outstanding sound regulation of acoustic waves in the extremely low frequency region. The structure is composed of an open waveguide and with a spiral throat tube and a cavity. The acoustic structure excites Helmholtz and Fabry-Perot resonances in labyrinth cavity structures, coupling of an open waveguide, which produce Fano-like resonances respectively and a broadband low-transmission spectrum in the 120–3100 Hz range. During sound regulation, the existing open waveguide can also maintain natural ventilation through the structure. In addition, the sound transmission properties are shown to be sensitive to the structural parameters, which can be used to provide a tunable sound control method for acoustic devices.

International audience; This paper presents a novel trade-off chart to support the design of multilayer acoustic packages. In this multi-objective problem, a designer has to specify a combination of layers from a set of available acoustic materials and thicknesses. Material types may include porous, mass-weighted, facing, among others. The combination must meet requirements in terms of sound absorption, sound transmission loss, cluttering, mass, etc. While predictions and analyses can be made on predetermined multilayer acoustic packages using the transfer matrix method, statistical energy analysis, finite elements methods or modal analysis, comparing a large number of possible combinations is cumbersome. On the other hand, optimization methods can be used to identify optimal thicknesses or material properties for a given layer combination, but the obtained solution may not be industrially relevant since, in general, only a limited set of acoustic materials and layer thicknesses exist commercially. In this paper, a new design methodology is proposed, which takes into account only the feasible combinations and provides guidelines for compromises between different performance parameters. The three-step methodology is demonstrated through a case study inspired by the automotive industry. First, relevant categories of layer configurations are defined, and following these patterns, all possible combinations of materials from a given inventory are calculated and stored in a database. Then, for selected performance parameters, the Pareto set of "better combinations" is identified. Finally, the "better solutions" are displayed on a trade-off chart through utility functions that allow weighing the different performance parameters. The tool developed for doing so is applied to the case study, and two example situations are presented. For each situation, the trade-off chart provides several suitable solutions, which are discussed. The use of this new tool effectively induces gains of time at the early stage of design, when it is most crucial.; Ce papier présente une nouvelle carte de compromis pour aider à la conception de solutions acoustiques multicouches. Dans ce problème multi-objectif, un concepteur doit spécifier une combinaison de couches à partir d'un jeu de matériaux et d'épaisseurs disponibles. Les types de matériaux peuvent inclure des matériaux poreux ou lestés, ou des couches de protections, par exemple. La combinaison doit répondre à des exigences d'absorption acoustique, de perte par transmission, d'encombrement, de masse, etc. Bien que des prédictions et des analyses puissent être réalisées pour une solution acoustique multicouche donnée en utilisant la méthode des matrices de transfert, l'analyse statistique énergétique, la méthode des éléments finis ou l'analyse modale, comparer un grand nombre de combinaisons possibles est complexe et coûteux. D'autre part, les méthodes d'optimisation peuvent être utilisées pour identifier les épaisseurs et les propriétés matériau optimales pour une combinaison de couches données, mais la solution obtenue peut ne pas être pertinente d'un point de vue industriel puisque, de manière générale, les matériaux acoustiques et les épaisseurs disponibles commercialement sont limités. Dans ce papier, une nouvelle méthodologie de conception est proposée, qui prend en compte uniquement les combinaisons réalisables et qui fournit des lignes directrices pour des compromis entre différents critères de performance. La méthodologie, composée de trois étapes, est présentée à travers un cas d'application inspiré par l'industrie automobile. Dans un premier temps, des catégories de configurations multicouches pertinentes sont définies, et toutes les combinaisons possibles respectant ces configurations avec un inventaire de matériaux donné sont calculées et stockées dans une base de données. Puis, pour des critères de performance choisis, le front de Pareto des « meilleures combinaisons » est identifié. Finalement, les « meilleures solutions » sont représentées sur une carte de compromis à l'aide de fonctions d'utilité qui permettent de pondérer différents critères de performance. L'outil développé est appliqué au cas d’application, et deux situations types sont présentées. Pour chaque situation, la carte de compromis fournit plusieurs solutions pertinentes, qui sont discutées. L'utilisation de ce nouvel outil permet un gain de temps aux étapes initiales de la conception, là où cela est le plus crucial.

A theoretical modelling approach is proposed for the vibroacoustic problem of sound transmission across a rectangular double-wall panel clamp mounted on an infinite rigid baffle with magnetically connected stiffness. The magnetic stiffness is derived based on interaction energy between the two rectangular magnets attached to the clamped plates. The exact solution for the vibration of the clamped double plates is taken into account by the method of modal function, and the dynamic response of the structures is obtained by employing the weighted residual (Galerkin) method. This method enabled the coupling of the acoustic and the magnetic stiffness of the link to be done effectively. The accuracy of the theoretical predictions is checked against existing experimental data, with good agreement achieved. The model is then compared with the theoretical formulation in a duct based on a low-frequency range with and without magnetic stiffness. The sound transmission loss (STL) of the two models agrees perfectly in the first resonance, but the mass–air–mass resonance frequency for the current model tends to shift towards a higher value. Furthermore, the influence of magnetic stiffness on the elevation angle and azimuth angle of the STL is investigated. The present method is suitable for double-panel systems with connecting stiffness for practical plates and is applicable for both low- and high-frequency ranges.

This paper concerns the use of the Wave and Finite Element (WFE) method for predicting sound transmission through, and radiation from, an infinitely long cylindrical structure. The formulation is general and can be used to analyse acoustic radiation or transmission due to arbitrary internal or external excitation. The WFE method involves modelling a small segment of a structure using traditional Finite Element (FE) methods. The mass and stiffness matrices of the segment are then used to calculate the response of the structure to excitation. The WFE approach for calculating sound transmission is validated by comparison with analytic solutions for three example problems: (1) the internal sound field produced by an acoustic source exterior to a thin-walled cylinder, (2) the radiation from a thin-walled cylinder due to excitation from a point force acting on the inner surface and (3) sound transmission through an orthotropic cylinder. In order to demonstrate the usefulness of the approach, the WFE method is then used to predict sound transmission through, and radiation from, more complicated cylindrical structures, for which an analytical model would be difficult to develop.

For industrial applications, the scalability of a finalised design is an important factor to consider. The scaling process of typical membrane-type acoustic metamaterials may pose manufacturing challenges such as stress uniformity of the membrane and spatial consistency of the platelet. These challenges could be addressed by plate-type acoustic metamaterials with an internal tonraum resonator. By adopting the concept of modularity in a large-scale design (or meta-panel), the acoustical performance of different specimen configurations could be scaled and modularly combined. This study justifies the viability of two meta-panel configurations for low-frequency (80–500 Hz) noise control. The meta-panels were shown to be superior to two commercially available noise barriers at 80–500 Hz. This superiority was substantiated when the sound transmission class (STC) and the outdoor-indoor transmission class (OITC) were compared. The meta-panels were also shown to provide an average noise reduction of 22.7–27.4 dB at 80–400 Hz when evaluated in different noise environments—traffic noise, aircraft flyby noise, and construction noise. Consequently, the meta-panel may be further developed and optimised to obtain a design that is lightweight and yet has good acoustical performance at below 500 Hz, which is the frequency content of most problematic noises.

It has been long considered that air and bone are the two major mediators that conduct sounds to the inner ear. In 2004, Hosoi found that vibration of aural cartilage, generated by placing gently a transducer on it, could create audible sound with the same level of clarity as air- and bone-conduction sound. He thus proposed the term "cartilage conduction" for this concept. This research identified a third mediator for sound conduction to the inner ear. Hosoi also proposed the development of novel communication devices, such as hearing aids, telephones, etc. using his findings. For cartilage conduction, three sound pathways can be assumed. The transducer vibration may cause airborne sound which passes into the external auditory canal through the canal entrance (direct air pathway). Alternatively, the vibration at the cartilage may generate audible sound in the external auditory canal (cartilage-air pathway), or propagate directly to the inner ear through the skull bone (cartilage-bone pathway). A series of studies has illustrated that the cartilage-air pathway is dominant for hearing sensations in listeners with normal ears. The cartilage-bone pathway works for patients with bony aural atresia. A fourth pathway, the fibrotic-tissue pathway, is considered to act in the case of fibrotic aural atresia. In this review, we summarize this series of studies and discuss the nature of cartilage conduction.

The propagation of sound across closely coupled narrow rectangular cavities in an infinitely long duct is studied numerically using finite-element simulation and the method of mode matching in the present investigation. Sound frequencies below the first cut-off frequency of the main duct are the focuses. Results show that the middle region of the coupled cavity section plays the most important role in affecting the spectral characteristics of sound transmission across the coupled cavities. It is also found that there exists a critical frequency above which a coupled cavity section can offer reasonably good sound transmission loss. In addition, similarity in this stopband cut-on frequency across coupled cavity sections of different dimensions is established empirically after the introduction of a new length scale. The corresponding frequencies of the symmetrical non-offset coupled cavity sections are also a vital parameter in the scaling. Two frameworks are developed to predict the stopband cut-on frequencies. Both of them are able to give predictions with accuracy to within engineering tolerance.

The head-related transfer function (HRTF) describes the sound transmission characteristics from a sound source to a listener’s ears. Recently, spherical harmonic decomposition has been extensively used for modeling the HRTF spatial patterns. Despite its advantage of approximating the coarse structure of HRTF spatial variations with modeling up to a low order, there are still some limitations since spherical harmonics take significant values in all directions. First, rapidly changing HRTF spatial variations in some local regions may require modeling up to a rather high order; this is not wise in terms of the modeling efficiency. Second, the expansion coefficients of the spherical harmonics describe the spatial frequency of the target dataset in all directions, and thus have difficulties in revealing the direction dependent HRTF characteristics. In this study, a method for locally modeling HRTF spatial patterns is proposed based on spherical wavelets, which take significant values only over a local region on the sphere. Results of numerical experiments show that our proposed method yields smaller approximation errors than the conventional method when representing HRTFs inside the local regions under evaluation. Furthermore, the expansion coefficients in the proposed method could well correspond to the HRTF local features on the sphere, which makes it a useful tool for the analysis and visualization of HRTF spatial patterns.

This paper presents an analytical study on the sound transmission loss characteristics of sandwich plate with different truss cores under external mean airflow. Three types of truss cores are considered, which include pyramidal core, tetrahedral core and 3D-kagome core. The sandwich plate is immersed in a mean airflow of velocity tangential to the acoustically deformed boundary and it is impinged by a plane sound wave in the incident acoustic field. By applying velocity continuity condition at fluid–structure interfaces, the coupling of fluid–structure interaction is described analytically. The validity and feasibility of the proposed theoretical model are verified by comparisons with numerical simulation results calculated by commercial finite element software (LMS Virtual.Lab). Based on the developed theoretical model, the influences of the truss core radius and height, different truss core types, external mean flow and material combination types on sound transmission loss are subsequently presented.

An artificial neural network (ANN) technique was applied to predict the sound insulation properties of ultrafine glass wool mats. Based on an experimental database for glass wool mats, sound transmission loss (STL) in the frequency of 1000 Hz, 2000 Hz and 4000 Hz were successfully calculated by a well-trained ANN. The structure 3 – [5]1 – 3 with the BR training algorithm was the most adaptive model in this paper, which was proved by comparing the mean relative error. By comparing the predicted results from ANN with measured data, it was demonstrated that the model gives predictions that are reasonably close to direct measurements. Three-dimensional planes for the predicted sound insulation properties as a function of thickness, areal density and resin content were established. The predictive quality was pretty satisfactory, which can be modified furthermore by enlarging the database range.

This paper focuses on prediction of the sound pressure level inside a vehicle by using statistical energy analysis (SEA) and control of the noise within limited trim materials for vehicle weight reduction. To this end, a vehicle SEA model was developed considering the effects of the SEA parameter uncertainties on the prediction results. Thereafter, the contributions of the sound transmission losses of several vehicle components and the absorptivity of the vehicle interior to the sound pressure level were identified. Global sensitivity analysis was performed to evaluate both the effects of the SEA parameter uncertainties and the contribution of the acoustical performance. Only the most influential SEA parameters were calculated or measured to reflect the characteristics of the acoustic material. Our results revealed that the sound pressure levels calculated by using the simplified SEA model agreed well with the measured values. Finally, based on the influences of the acoustic performances of the vehicle components on the interior noise, the design of the trim materials on the dash, which was one of the sensitive components, was modified and compared to the initial design and conventional lightweight design in terms of interior noise and weight.

In this paper, an ultralightweight sandwich panel with closed octahedral core is proposed, which demonstrates excellent acoustic property of sound transmission loss as well as great mechanical performance. Simulation models are established with considerations of acoustic-structure interactions. The validity of simulation calculations is checked against experimental measurements with the tested specimens provided by additive manufacturing. Numerical discussions are conducted to demonstrate the effects of incident angles, topological parameters, and so on which should be helpful for practical design. This novel class of sandwich structure with closed octahedral core constructions shows promising engineering applications.

The high-speed train (HST) interior noise in low, middle and high frequency bands is predicted in different simulations due to the limitations of current numerical methods. In this paper, a new method named statistical vibration and acoustic energy flow (SVAEF) is proposed to predict full-spectrum HST interior noise directly. In the SVAEF theory, interior noise is solved in the form of energy flow, and panel vibration responses caused by mechanical and acoustic excitations are assumed to satisfy the linear superposition principle. The acoustic energy of exterior sound sources is mainly attenuated by the carriage structure in the equivalent form of sound transmission loss, while the mechanical vibration energy flows inside carriage structure and interior acoustic cavities. The interior acoustic responses are calculated under a dynamic equilibrium of the whole energy flow. Initially, a HST carriage model is established based on SVAEF theories. And all the subsystem parameters and exterior excitations are acquired properly through the measurements, simulations and empirical formulas. Among them, inverse-fast Fourier transform (IFFT) and rigid multi-body dynamics are used for track irregularity excitations and contact force, while the wheel-rail rolling noise is extracted and verified with the sound scattering effect of carriage surfaces considered. The distributions of aerodynamic noise are calculated by the hybrid method of Reynolds-averaged Navier-stokes (RANS) and non-linear acoustic solver (NLAS) approach with the pantograph system, the bogie and windshield completely considered. In addition, the equipment noise under the carriage is measured as one of acoustic excitations and the vibration of carriage panels is measured to extract mechanical excitations. Finally, the interior noise is predicted through SVAEF and compared with the measurements and other prediction methods. The results indicate that the trend of SVAEF predictions is in better agreement with measurements in the whole frequency bands, and the deviations of overall sound pressure level (OASPL) are much smaller. In conclusion, the effectiveness and accuracy of SVAEF method have been verified in the full-spectrum prediction of HST interior noise.

Producing practical designs for light-weight timber-framed structures that achieve high sound isolation remains a challenging task, in part because of the lack of models that can accurately predict the sound transmission through proposed designs. This work develops detailed modeling of structural vibration in timber floor/ceiling systems, from which sound transmission in the low-frequency regime (10–150 Hz) can be computed, as a design tool for producing practical timber floor/ceiling details that achieve high isolation for low-frequency sound. The mathematical model uses a variational formulation that enables straightforward modeling of complex composite structures, and introduces the notion of coupling layers to model the movement between joined materials that occurs with practical bonding methods, thereby improving on existing models that assume either perfectly bonded or perfectly slipping interfaces. The composite model structure is assembled only at the computational step, giving an efficient computational scheme that also fits well into the design-development cycle. Results from a parallel experimental program are used to validate the model and to determine effective coupling and damping parameters. The influence of coupling parameters is shown for an example floor, demonstrating that finite slippage at joints is required for the model to predict low-frequency vibration in practical constructions.Producing practical designs for light-weight timber-framed structures that achieve high sound isolation remains a challenging task, in part because of the lack of models that can accurately predict the sound transmission through proposed designs. This work develops detailed modeling of structural vibration in timber floor/ceiling systems, from which sound transmission in the low-frequency regime (10–150 Hz) can be computed, as a design tool for producing practical timber floor/ceiling details that achieve high isolation for low-frequency sound. The mathematical model uses a variational formulation that enables straightforward modeling of complex composite structures, and introduces the notion of coupling layers to model the movement between joined materials that occurs with practical bonding methods, thereby improving on existing models that assume either perfectly bonded or perfectly slipping interfaces. The composite model structure is assembled only at the computational step, giving an efficient comput...

Vibration measurement in building acoustics can help understand and estimate different physical phenomena for both researchers and practitioners. Sound insulation and flanking sound transmission are just some of these phenomena and interesting information can be obtained from wall vibration. Different approaches are available in terms of instruments and techniques, ranging from laser interferometry to single axis accelerometers. The latter are simple and cost-effective solutions because they allow many practitioners to use them in an affordable way. In order to deal with the problem in a more efficient way, there is a need to employ a less intrusive mounting technique and we therefore performed a study of the handheld probe solution in detail. Calibration and theoretical data on probe tips attached to different sensors is extremely difficult to find in relation to frequency response, resonance or repeatability. A new and simple sensor characterization procedure is presented to study deviations in probes, depending on the mounting technique and its comparison to a more robust wax fixing method. Handheld probes modify accelerometer response, mainly due to the probe length and the material. Sensor size, weight and connector location were also observed as influencing variables, in addition to others, such as operator hand tremor and the way the sensor is held. Nevertheless, a study of all these variables would provide a very complex model and we therefore used a statistical approach to simplify the characterization tasks. In building acoustic vibration, a Gaussian probability distribution is usually assumed in the collected data, although not being true in all cases. An innovative Bootstrap approach was thus employed in this study without any assumptions on data probability distribution. Bootstrap is a non-parametric method that provides further information than typical average values on a particular experimental population, when the real population is unknown and difficult to estimate. Bootstrap statistical mean and its confidence interval are used as performance indexes. Ninety probe types and sensor set-ups were characterized according to their frequency response and repeatability in a real environment, as compared to regular Wax fixing. Probes show less repeatability than wax or simply handheld broadband techniques, but 95% Bootstrap statistical mean confidence intervals were less than 0.5 dB in a low frequency range, up to a maximum of 3.8 dB at higher frequency bands of interest. Higher deviations are found in system resonance. Nevertheless, uncertainty values on repeatability in building acoustics are not far from these values. A good similarity is found in a probe useful bandwidth ranging from 50 Hz to 800 Hz–1 kHz, depending on the probe’s features. Bootstrap statistical mean is useful to correct measurements of deviations in frequency response. This handheld vibration probe data approach can provide more efficient resource management in real test situations.

In this study, an analytical model is proposed to investigate the sound transmission loss through multi-walled plates with air layers or decompression air layers, under the diffuse incidence field. Using the present approach, the influences of various parameters, such as the wall thickness, the decompressed air and the thickness of air space, on the sound transmission loss through are simulated and discussed in detail. It is seen that, due to the wave frequency of mass-air-mass resonance between double-walled glass plates, the sound transmission loss of the plates can be improved at low frequency range. The sound transmission loss tends to increase with decreasing air pressure because the sound is not transmitted through vacuum space. The design method can be used to investigate the effect of various geometric and material parameters on the sound transmission loss. The advantage of the simulation procedure is easily used for designing the layer structures with different parameter to improve the sound insulation effect.

The square timbers of larch having cross section of 90 mm × 90 mm were glued laterally to be formed 1,200 mm × 2,400 mm panels which were used as cores for CLT wall panels. Then, structural plywood panels having size of 1,200 mm × 2,400 mm were used as cross band covering the small square timber cores to manufacture CLT wall panels. The sound absorption rate of CLT wall panels and polyester board attached CLT wall panels were investigated. The mean sound absorption coefficients of the former and the latter in the frequency range of 100-6400 Hz were 0.21 and 0.74, respectively. The noise reduction coefficients (NRC) of those were 0.21 and 0.40, respectively. Also, the mean sound transmission loss of CLT wood panel in the frequency range of 50-1600 Hz was 45.12 dB and that value at the frequency of 500 Hz was 42.49 dB. It was suggested that the polyester board attached CLT wall panels could be used as housing wall because of its high sound absorption rate and high sound transmission loss.

A Chebyshev-Ritz based analytical model is proposed to investigate I-junction within the structural–acoustic model of a cascaded rectangular plate–cavity system. By considering of the structural interconnection force and the moment at edges and structural-acoustic interaction on the interface, the structural and acoustic systems are coupled. Two-dimensional and three-dimensional Chebyshev Polynomial series are used to present the unknown panel displacements and the sound pressure field variable inside the cavities, respectively. The effectiveness and correctness of the proposed model on an I-junction in a typical marine offshore platform are verified with those calculated from Finite Element Analysis. The influence of boundary conditions, structural coupling, plate properties, and size of the source-to-receiver cavities on the offshore platform on structure-borne sound transmission are analyzed and addressed. Numerical examples are simulated for several different configurations. It is shown that the boundary conditions, structural coupling manner, plate properties, and the volume ratio of the source-to-receiver cavity will change the structure-borne sound transmission characteristics of the cascaded rectangular plate–cavity system. With the proposed approach, a better prediction can be obtained for structure-borne sound transmission via proper tuning of the cascaded rectangular plate–cavity system on the offshore platform.

The noise suppression problems within ducts are widespread in aero engines, gas turbines, blowers and various mufflers. It has been well demonstrated that the Cremer impedance can maximize the propagating damping by degenerating the lowest order mode pair into a single mode, and consequently maximize the sound attenuation in both circular and rectangular ducts, however, the Cremer impedance of annular ducts is still unsettled. Therefore, the Cremer concept is further developed to theoretically optimize the acoustic impedance for annular ducts with two degrees of freedom, i.e. inner and outer liner impedances. Through decoupling successfully the radial wavenumber and impedance, the branch point equations are derived in the presence of grazing flow to solve the triple or double eigenvalues, which can be used to design simultaneously the optimal inner and outer impedances. A parametric study is conducted to investigate the effect of the Helmholtz number (kb), the circumferential mode order (m), the radius ratio (RR) and the liner configurations on the optimum radial wavenumber, Cremer impedance and sound transmission loss (TL). Some conclusions are drawn. First, the double eigenvalue solutions can give optimum impedance under more general conditions than triple eigenvalue solution. At small RR, the solutions of outer wall approximate to Cremer impedance of circular ducts, and at large RR and m = 0, the double eigenvalue solutions of both inner and outer walls are identical to Cremer impedance of rectangular ducts with zero transverse mode. Second, with the decrease of kb and the increases of m and RR, the optimum TL exhibits a general tendency of growth. Third, higher TL gain leading by inner liner can be achieved for larger RR and lower m, and whether the inner liner works effectively depends on the sound energy densities near inner and outer walls. Fourth, the RR and kb have larger impacts on the optimum TL than m, thus needing to be given priority to consider in design, the utilization of inner liner needs to comprehensively balance the effectiveness, economical efficiency and the realizability.

Pyramidal lattice sandwich structure (PLSS) exhibits high stiffness and strength-to-weight ratio which can be effectively utilized for designing light-weight load bearing structures for ranging from ground to aerospace vehicles. While these structures provide superior strength to weigh ratio, their sound insulation capacity has not been well understood. The aim of this study is to develop numerical and experimental methods to fundamentally investigate the sound insulation property of the pyramidal lattice sandwich structure with solid trusses (PLSSST). A finite element model has been developed to predict the sound transmission loss (STL) of PLSSST and simulation results have been compared with those obtained experimentally. Parametric studies are then performed using the validated finite element model to investigate the effect of different parameters in pyramidal lattice sandwich structure with hollow trusses (PLSSHT), revealing that the pitching angle, the uniform thickness and the length of the hollow truss and the lattice constant have considerable effects on the sound transmission loss. Finally a design optimization strategy has been formulated to optimize PLSSHT in order to maximize STL while meeting mechanical property requirements. It has been shown that STL of the optimal PLSSHT can be increased by almost 10% at the low-frequency band. The work reported here provides useful information for the noise reduction design of periodic lattice structures.