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A three-dimensional modified Fourier series method is applied to study the acoustic characteristics of the trapezoidal cavity and coupled cavity with various impedance boundary conditions. The formulation is constructed to describe the cavity systems based on the energy principle. The admissible sound pressure function is set to a Fourier cosine series and supplementary functions. These supplementary functions can eliminate the discontinuous or jumping phenomenon in the boundaries. The trapezoidal cavity can be transformed into regular rectangular cavity by coordinate transformation. The triangular cavity can be obtained by changing the dimensions of the trapezoidal cavity. The coupled cavity consists of two irregular triangular cavities and the coupling interface is regarded as a non-dissipative surface. The accuracy and convergence of the present results are verified by comparison with the results obtained by finite element calculation and experiment. The natural frequencies and mode shapes of the trapezoidal cavity and coupled cavity are studied. Besides, the sound pressure response under monopole sound source excitation is obtained. What’s more, some results are obtained in the basis of effects of various factors on acoustic characteristics, such as shapes, geometric parameters and impedance values. These results provide a benchmark for the future researches.

The vibration of an aluminum hemispherical shell filled with inviscid compressible fluid is considered. The modal frequencies, damping ratio and mode shapes of the shell are experimentally determined under both empty and fully-filled conditions. A numerical simulation based on the finite elements is conducted to be verified with the experimental modal analysis using a roving hammer-impact test. The finite element analysis of the fluid and the solid shell has been carried out implementing the fluid-solid interaction formulation analysis. The modal frequencies of modes are in good agreement with the numerical simulations. The modal frequencies decrement is observed in both numerical and experimental modal analysis as the impacts of the fluid-structure interaction on the hemisphere shell vibration. The simulated numerical mode shapes and the experimental ones are in close agreement and show that the fluid-solid interaction condition eventuates modal shape transformation.

The Modal FxLMS algorithm is recently proposed for reduction of global level of noise in vibro-acoustic cavities. The algorithm minimizes acoustic potential energy expressed in modal domain which allows a choice of acoustic modes whose modal amplitudes are desired to be minimized. The working of the algorithm and its effectiveness has been demonstrated previously through a numerical study and an experimental study is required to test the effectiveness of the algorithm in practice. To meet this objective this paper presents an experimental study of this algorithm for global active noise control in a rectangular box cavity. The algorithm utilizes modal filtered reference signals and modal amplitudes of the selected acoustic modes of the cavity. To identify modal filtered reference signals, modal secondary paths are utilized. In the present study, modal secondary paths are identified using experimentally identified physical secondary paths and acoustic mode shapes. Modal amplitudes of the acoustic modes are identified on the basis of acoustic pressure measurements from eight microphones suitably placed throughout the cavity. The performance of the algorithm is studied under the presence of acoustic and structural disturbances using one or two control loudspeakers. The active control is carried out at harmonic frequencies coinciding with cavity-controlled resonances and panel-controlled resonances. It is found from the experimental results that the Modal FxLMS algorithm is successful in reducing modal amplitudes of the selected acoustic modes. When all the significantly contributing acoustic modes are chosen, a reduction in global level of noise is observed at cavity as well as panel controlled resonances.

Numerical evaluation of exact high-order modes of uniform Timoshenko beams is a classic problem in the field of acoustics and vibration. In the classic method, however, the determinant of the frequency matrix dominated by hyperbolic functions can increase exponentially and quickly reach the precision limitation of a computer. As a result, a bottleneck occurs in the evaluation of high-order modes due to round-off errors. Addressing this bottleneck, this study proposes an enhanced classic method relying on a segmenting scheme for evaluating exact high-order modes of uniform Timoshenko beams. With the segmenting scheme, a uniform Timoshenko beam is uniformly segmented into several segments, whereby the hyperbolic functions involved in the determinant of the frequency matrix become much smaller for the same given frequency. Accordingly, under the fixed precision limitation in a computer, higher-order modes can be obtained. The capacity of this enhanced classic method for evaluating exact high-order modes is validated by scenarios of a uniform Timoshenko beam with different numbers of segments. The results show that the high-order modal frequencies and mode shapes can be properly obtained. The accuracy of the modal frequencies is verified by the well-established exact dynamic stiffness method with the Wittrick-Williams algorithm. The results show that the modal frequencies are highly accurate. Applied to beams of different materials, the artificial segmenting is more suitable than the natural segmenting in evaluating high-order modes.

In this study, an efficient damage detection technique using the differential evolution (DE) algorithm and vibration data is proposed to properly detect the locations and extents of multiple damages of truss structures. The general equilibrium equations in which the reaction forces at notes are taken into account are considered. The compatibility equations in terms of forces are presented using the singular value decomposition (SVD) technique and then the extended equations of motion are developed based on the force method. As an optimization algorithm, the differential evolution (DE) algorithm is utilized and the objective function for damage detection is based on vibration data such as natural frequencies and mode shapes. Three numerical examples for planar and space truss structures are considered to verify the effectiveness and practical applicability of the present study. The numerical results show that the proposed method based on DE and vibration data can provide a reliable tool on determining the locations and extents of multiple damages of truss structures when it compares with those obtained from the genetic algorithm.

This paper presents a theoretical investigation on actively controlling the low frequency sound absorption of large-sized micro-perforated panel absorber (MPPA) by using point source placed in the cavity. The large sized active MPPA is an easily implemented and cost-effective scheme for achieving superior low frequency sound absorption in large area. The modal analysis approach is used to establish the theoretical model of such active MPPA. The physical mechanism of active control is analyzed and some physical insights are summarized. Based on these conclusions, the error sensing strategy of the large sized active MPPA is also constructed. Finally, experimental tests are carried out to validate the theoretical modeling and findings. Results show that the sound absorption performance can be significantly improved after control in a wide low frequency range below the cutoff frequency. The optimal position of the point source is at the central of the cavity section, in which case the cutoff frequency is the largest and depends on the length of the short side of the active MPPA. The control mechanism of sound absorption improvement is to enhance the Helmholtz type resonant absorption by suppressing the cavity sound field. The high order cavity mode (except for (0,0,0) mode) has no contribution to sound absorption improvement due to the symmetrical property of their mode shape. The pressure release (PR) and impedance matching (IM) strategies are still applicable for the large sized active MPPA. Relative small sized cavity or low frequency excitation can guarantee the uniformity of the cavity sound field after control, which is conducive to achieve remarkable improvement of sound absorption.

Modeling and free vibration analysis of bolted joined cylindrical-cylindrical shell were presented in this paper. First, a new analytical model was established for bolted joints. Second, based on Sanders’ shell theory, the dynamic equation of substructure of the assembly structure was formed. Then, by using the connection condition, into which the coupling stiffness between the segments was considered, the vibration differential equation of the assembly structure was established. Finally, the vibration characteristics of bolted joined cylindrical-cylindrical shell were obtained. To test the accuracy of the present method, the frequencies and mode shapes under some special connecting condition were examined with the results obtained by ANSYS and a good agreement was shown. Further, the number of bolts, connecting stiffness and length ratio of the two segments have a significant influence on natural frequency parameters and mode shapes of symmetrical and unsymmetrical structures. The results reveal the vibration characteristics of bolted joined cylindrical-cylindrical shell and are presented to provide useful information for future research. Moreover, some new results would be of signification for assembly structure design and vibration control.

Wave based method (WBM) is presented for vibration analysis of double-walled cylindrical shells coupled by annular plates. To establish the governing equation, the double-walled shell is divided into several cylindrical shell segments and annular plates according to junctions of discontinuities, and they can be easily synthesized through continuity conditions at the junctions. Flugge shell theory and thin plate theory are utilized to describe motions of cylindrical segments and annular plates, displacements of which are expanded as wave functions. In addition, artificial springs are employed to restrain displacements at boundaries to uniformly consider elastic and classic boundary conditions. To test the validity of WBM, free and forced vibration results of WBM are compared with those of literature and finite element method, which demonstrates high accuracy of present method. Some mode shapes are also given for visual understanding. Furthermore, effects of elastic boundary conditions and annular plates on free and forced vibrations are investigated. Results show that axial and circumferential displacements are of great effect on fundamental and beam mode frequencies, and effects of the number of annular plates are obviously greater than the thickness of annular plates. The results of present paper can be used as benchmarks for further researches.

The actual ocean is an uncertain acoustic propagation environment. For the localization algorithms that rely on the precise ocean environmental parameters, the environmental mismatch problems will exist and performance degradation may be very serious. In the uncertain ocean environment, the uncertainties of sound field will have different effects on different normal modes propagating in the sound field, thus analysis of the mismatch characteristics of normal modes affected by uncertain environmental parameters can provide technical guidance for practical engineering applications. Based on the shallow-water acoustic propagation model, this paper simulates and analyzes the mismatch results of the modal depth eigenfunction and the horizontal wave number of each normal mode under conditions of environmental mismatch. Research indicates that the influence of different environmental parameters on normal modes in the sound field is not exactly the same. It was found that the sound-speed profile and seawater depth affect significantly, followed by sediment sound speed, the other parameters appear to be relatively minor importance.

To investigate the frequency response characteristics of a push–pull electrostatic speaker (60-mm diameter) and free-edge-like piezoelectric speakers (68-mm and 73-mm diameters), this study was employed optical and acoustic measurements from 20 Hz to 20 kHz. The optical measurements of displacement amplitude and mode shape were used to predict sound pressure levels (SPLs). Comparisons with measured SPL values were used to verify the predictions. When using a mesh with acoustic flow resistance, i.e., unless damped, the electrostatic and piezoelectric speakers both produced numerous resonant frequencies. The two evaluation methods produced SPL values that were in good agreement. The piezoelectric speakers produced jagged SPL curves with peaks steeper than those of the electrostatic speaker. At the first axisymmetric mode, the electrostatic speaker was affected by acoustic resistance, which resulted in the following quality factor (Q) values: without mesh (Q = 6.16) and using a mesh with specific acoustic resistance of 145 rayl (Q = 1.74). By contrast, the piezoelectric speakers at modes (0, 1)–(0, 4) were unaffected by acoustic resistance, which resulted in Q values of 10–11, regardless of whether mesh was applied. Because higher Q performs larger acoustic response and lower Q presents wide broadband, this study concluded that the characteristics make electrostatic speakers suitable for headphones and piezoelectric speakers suitable for audio signaling devices.

Variability in the dynamic response of assembled structures can arise due to variations in the contact conditions between the parts that conform them. Contact conditions are difficult to model accurately due to randomness in physical properties such as contact surface, load distribution or geometric details. Those properties can vary for a given structure due to the assembly and disassembly process, and also across nominally equal items that are produced in series. This work focuses on modeling the contact between small light-weight plastic pieces such as those used in the hearing aid industry, where the vibrational behavior of the structures within the hearing frequency range is critical for the performance of the devices. A procedure to localize the most probable contact areas and determine the most sensitive contact points with respect to variations in the modes of vibration of the assembled plastic parts is presented. The procedure uses a gradient-based optimization strategy that updates the stiffness constants of a number of contact spring elements to match experimental data. By identifying the contact parameters for several sets of experimental data measured under varying contact conditions, the variability of the contact parameters can be characterized.

In this paper, Resonance Ultrasound Spectroscopy (RUS) is used to invert the elastic properties of components with complex shapes from a limited selection of mode matched frequencies. RUS is based on the unique relationship between the vibrational resonance response (resonance frequencies and mode shapes) of a component and its set of material properties, geometry, and boundary conditions. The study is conducted on 3 nominally identical components that have geometric imperfections due to the manufacturing process. The study reveals that an accurate characterization of the shape is critical to the success of the RUS process. The RUS process presented in this paper also relies on matching measured and computed vibrational mode shapes, in addition to the resonance frequencies. This strategy enables using high-order modes with complex modal information, in a frequency range with high modal density where modal identification based on the resonance frequencies alone would be challenging. This approach contrasts with the traditional approach of matching a number of resonance frequencies in sequential order. With the proposed approach, the elastic constants for the three components are similar, consistent with values found in the literature, and lead to small error of the RUS inversion, despite variations in the shapes and the resulting changes in the resonance response of the components.

For decades, modal analysis has been a tool to gain insights in the vibrational and acoustical behavior of music instruments. This study provides a critical comparison of various experimental modal analysis approaches with the violin as a case study. Both contact and non-contact excitation and different acquisition approaches are considered. The influence of different boundary conditions (clamped, supported, free/free) on the vibrational response of the violin is investigated. The response is analyzed to extract relevant modal parameters (frequency, damping and mode shape) within the frequency range of 0–1000 Hz. The performance of the different approaches is evaluated in terms of (i) signature vibration modes, (ii) experimental reproducibility, (iii) contact requirement and (iv) cost of required equipment. Two optimal approaches are proposed for performing modal analysis on violins: a contact method for use in the violinmaker’s practice, and a non-contact method for use with fragile instruments.

In this paper, the free and forced vibration analysis of circular cylindrical double-shell structures under arbitrary boundary conditions is presented. This is achieved by employing the improved Fourier series method based on Hamilton’s principle. In the formulation, each displacement component of the cylindrical shells and annular plates is invariantly expanded as the superposition of a standard Fourier series with several supplementary functions introduced to remove the potential discontinuities of the original displacement and its derives at the boundaries. With the introduction of four sets of boundary springs at the coupling interfaces and end boundaries of the shell–plate combination, both elastic and rigid coupling and end boundary conditions can be easily obtained by assigning the stiffnesses of the artificial springs to certain values. The natural frequencies and mode shapes of the structures as well as frequency responses under forced vibration are obtained with the Rayleigh–Ritz procedure. The convergence of the method is validated by comparing the present results with those obtained by the finite element method. Several numerical results including natural frequencies and mode shapes are presented to demonstrate the excellent accuracy and reliability of the current method. Finally, a number of parameter studies concerning various end and coupling boundary conditions, different dimensions of shells and annular plates are also performed.

International audience; This work concerns the control of sound transmission through double laminated panels with viscoelastic core using semi-passive piezoelectric shunt technique. More specifically, the system consists of two laminated walls, each one composed of three layers and called sandwich panel with an air cavity in between. The external sandwich panel has a surface-mounted piezoelectric patches. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of some specific resonance frequencies of the coupled system. Firstly, a finite element formulation of the fully coupled visco-electro-mechanical-acoustic system is presented. This formulation takes into account the frequency dependence of the viscoelastic material. A modal reduction approach is then proposed to solve the problem at a lower cost. In the proposed technique, the coupled system is solved by projecting the mechanical displacement unknown on a truncated basis composed by the first real short-circuit structural normal modes and the pressure unknown on a truncated basis composed by the first acoustic modes with rigid boundaries conditions. The few initial electrical unknowns are kept in the reduced system. A static correction is also introduced in order to take into account the effect of higher modes. Various results are presented in order to validate and illustrate the efficiency of the proposed finite element reduced order formulation.

This paper presents an evaluation method for measuring the sound pressure level and mode shapes of tire cavity resonance by using a multi-microphone system. Two commercial tires were evaluated to compare abilities of noise suppression by means of this method in the range of the first resonance from 200 to 260 Hz. One tire was a special tire that suppresses tire cavity resonance with polyurethane foam mounted on the tire’s inner liner. The other tire was a normal tire with no polyurethane foam. The mode shape change from vertical to horizontal direction in both tires. However, the sound pressure level of the special tire was lower than the normal tire at all frequencies.

This paper studied the acoustic wave propagation in a waveguide with continuous right-angled corners, with emphasis on the effect brought by the distance between the corners. The numerical analyses showed that at middle to high frequencies, the transmission loss (TL) of a multi-cornered waveguide was 2–5 dB higher than that of single-cornered and varied with frequency. To explain the performance at peaks and dips in the TL curve, analyses on eigenmodes and sound intensity distribution were conducted. The performance of multi-cornered waveguides was experimentally investigated, which fit well with the numerical results. The present study indicates that, for a waveguide with continuous corners, its acoustic performance is not simply a “summation” of two individual single-cornered ones. Both the standing wave modes and the evanescent modes between the corners lead to its complicated frequency performance.

The NASA Langley Research Center Curved Duct Test Rig (CDTR) is designed to test aircraft engine nacelle liner samples in an environment approximating that of the engine on a scale that approaches the full scale dimensions of the aft bypass duct. The modal content of the sound in the duct can be determined and the modal content of the sound incident on the liner test section can be controlled. The effect of flow speed, up to Mach 0.5 in the test section, can be investigated. The results reported in this paper come from a study to evaluate the effect of duct configuration on the acoustic performance of single degree of freedom (SDOF) perforate-over-honeycomb liners. Variations of duct configuration include: asymmetric (liner on one side and hard wall opposite) and symmetric (liner on both sides) wall treatment; inlet and exhaust orientation, in which the sound propagates either against or with the flow; and straight and curved (outlet is offset from the inlet by one duct width) flow path. The effect that duct configuration has on the overall acoustic performance is quantified. The redistribution of incident mode content is shown, in particular the mode scatter effect that liner symmetry has on symmetric and asymmetric incident mode shapes. The Curved Duct Test Rig is shown to be a valuable tool for the evaluation of acoustic liner concepts.

Concrete causes substantial attenuation on ultrasonic guided waves during their propagation within a pipe. The circumferential position of the defect is even more difficult to detect in a concrete-covered pipe with a small diameter. This paper reports that the axial and circumferential positions of a circumference defect in a small-diameter concrete-covered pipe can be identified by moving the half-covered axial magnetised magnetostrictive patch transducer (AM-MPT) around the circumference of the pipe for subsequent measurements. First, the theory of normal mode expansion (NME) and demagnetisation is presented for the proposal of the nondestructive test (NDT) method and half-covered AM-MPT. Second, the NDT method based on NME is explained. Subsequently, the finite element models and experiments are applied to reveal the propagation of triggered and reflected non-axisymmetric guided waves L(M,2) to prove that the proposed method is applicable. Third, several frequencies of L(M,2) are compared to determine the best fit. The experimental results of pipes tested using half-covered AM-MPTs with different length–width ratios of iron cobalt patches proved that the greater the length–width ratio, the greater the amplitude of L(M,2) signals. These results support the theoretical results for the demagnetising field. The signals received from different circumferential positions of the pipe using AM-MPTs reveal that increasing the coverage of the transducer can improve the consistency of the signals received from the different circumferential positions. Next, the group velocity and attenuation characteristics of L(M,2) within the concrete-covered pipes were studied through experiments, with results matching the theoretical results. Finally, the experimental results proved that the proposed method could be utilised to determine the axial and circumferential positions of the defect in concrete-covered pipes. Moreover, the precision of the detection results can be improved by adding the monitoring position around the circumference of the pipe. It was demonstrated that the proposed method has potential to detect defects in concrete-covered pipes.

Acoustic Black Hole (ABH) has been attracting the ever-increasing attention from the scientific community as a passive, effective and lightweight solution for vibration and noise mitigations of vibrating structures. Most existing work, however, relies on numerical simulations using Finite Element models, except a few cases where alternative methods are attempted. In general, there is a lack of well-calibrated experimental benchmark solutions for model validations and phenomena assertions, especially in 2D cases where precise fabrication of ABH indentations with well-controlled thickness profile is a challenge. In this paper, a rectangular plate embodied with a symmetric circular ABH indentation is meticulously manufactured and experimentally tested in terms of eigen-frequencies, mode shapes, forced vibration response and radiated sound power in a baffled half-space. These results offer useful benchmark solutions for future ABH studies. In particular, experimental results show a high consistency with the ones predicted by the previously developed 2D Daubechies wavelet (DW) model.

The continuity condition is proposed for modeling and analyzing the vibration characteristics of sectional-laminated cylindrical thin shells with arbitrary boundary conditions. The orthogonal polynomials are used to describe the vibration displacements of the sectional-laminated cylindrical shell. Four sets of springs are applied to simulate arbitrary boundary conditions. The Donnell thin shell theory is employed to formulate the theoretical model. To test the convergence and accuracy of the present modeling method, free vibrations of sectional-laminated cylindrical shells are examined with clamped-clamped and simply-simply boundary conditions. The numerical results are compared with those obtained by using the finite element software ANSYS. The effects of the pre-assigned weighted parameters, the length ratio of the non-laminated cylindrical shell and the thickness ratio of inner and outer layers on natural frequencies and mode shapes are presented with arbitrary boundary conditions.

In the present paper, free axisymmetric vibrations of functionally graded circular plates subjected to a non-linear temperature distribution along the thickness direction have been studied on the basis of classical plate theory. The top and bottom surfaces of the plate are under uniform thermal environment. The mechanical properties of the plate material are assumed to be temperature-dependent and the plate is graded in thickness direction. The equations for thermo-elastic equilibrium as well as axisymmetric motion for such a plate model have been derived using Hamilton’s principle. Employing generalized differential quadrature rule, the numerical values of thermal displacements from thermo-elastic equilibrium equation and frequencies from the equation of motion for the lowest three modes of vibration have been computed for clamped, simply supported and free plates. The effects of the temperature difference at the surfaces together with material graded index and thickness of the plate on the frequencies have been investigated. The benchmark results for uniform and linear temperature distributions have been computed. For the validity of present considerations and the technique, frequency parameter has been compared for some special cases with published results obtained from other approximate methods.

In this paper, the directionality of sound radiated from a rectangular panel, attached with masses/springs, set in a baffle, is studied. The attachment of masses/springs is done based on the receptance method. The receptance method is used to generate new mode shapes and natural frequencies of the coupled system, in terms of the old mode shapes and natural frequencies. The Rayleigh integral is then used to compute the sound field. The point mass/spring locations are arbitrary, but chosen with the objective of attaining a unique directionality. The excitation frequency to a large degree decides the sound field variations. However, the size of the masses and the locations of the masses/springs do influence the new mode shapes and hence the sound field. The problem is more complex when the number of masses/springs are increased and/or their values are made different. The technique of receptance method is demonstrated through a steel plate with attached point masses in the first example. In the second and third examples, the present method is applied to estimate the sound field from a composite panel with attached springs and masses, respectively. The layup sequence of the composite panel considered in the examples corresponds to the multifunctional structure battery material system, used in the micro air vehicle (MAV) (Thomas and Qidwai, 2005). The demonstrated receptance method does give a reasonable estimate of the new modes.

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.

Some acoustical measurements on the jarana jarocha primera (first), a traditional Mexican instrument, a “one-piece” body instrument, in the coastal region of the Gulf of Mexico, are presented. Experimental mobility function, radiativity function, and some radiation patterns were obtained. Harmonic analysis and visualization techniques using both the finite element method and laser speckle-Chladni methods were made to obtain the lower deflection shapes of the soundboard. The experimental analysis using mobility function measurements of the lower resonances shows behaviour very similar to that observed in the classical guitar.

In this paper, free vibration response of stepped beams made from functionally graded materials (FGMs) is investigated. The beams are supported by various types of elastically end constraints. The differential transformation method (DTM) is employed to solve the governing differential equations of such beams in order to obtain natural frequencies and mode shapes. The power law distribution is used and modified to describe material compositions across the thickness of the beams made of FGMs. Two main types of the stepped FGM beams in which their material compositions can be described by using the modified power law distribution are selected to investigate their vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions, spring constants and material volume fraction are taken into investigation.

This paper presents the formulation and experimental validation of a numerical tool that can predict: (1) the external pressure loading due to impulsive sound generated by an outdoor point source and (2) the resulting fully coupled vibro-acoustic response at low frequencies of a two-dimensional building component (e.g. wood-framed wall with windows) backed by a rigid rectangular cavity. The model allows for the building component to have arbitrary geometry and boundary conditions. Assuming linear-acoustic propagation and acoustically rigid surfaces, the external pressure loading is computed with a three-dimensional numerical model, in the time domain, by combining the image-source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. The fully coupled vibro-acoustic response of the fluid–structure system is computed in the time-domain using a modal-decomposition approach. The natural frequencies and mode shapes of the structure are computed with a finite-element model based on shell theory. Acoustic natural frequencies and mode shapes of the cavity are computed analytically assuming hard-wall boundary conditions. The experimental validation of the numerical model is also presented. Experiments were conducted on wood-framed walls without and with a window using a speaker to generate N-waves and load the walls structurally. It is found that numerical simulations are in good agreement with experimental data for these two cases.

In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a cantilever beam with intermediate support is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function. By using boundary condition and continuity condition equations at intermediate support, the closed-form series solution of the second spatial derivative of the mode shapes can be determined based on DTM. Then the shapes of the designed modal sensors are obtained. Finally, numerical examples are given to demonstrate the feasibility of the proposed modal sensors for the cantilever beam with intermediate support.

The location of a vibration source within a machine is sometimes found to have a significant effect upon its radiated acoustic power. It is known that a simple reduction of vibration cannot always reduce the radiated acoustic power, so that treatments based on analysis of a structure’s vibration modes are not always effective. At the same time, radiation mode analysis is known to be a powerful tool for interpreting sound radiation since those modes are independent of a structure’s surface vibration. However, knowledge of the radiation modes alone cannot be used directly to understand the relationship between vibration source location and acoustic power radiation. In this paper, it is shown that the radiation mode concept can be extended to understand the relationship between acoustic power and driving force distribution by considering the product of the structure’s mobility matrix and the radiation modes: the resulting functions are here defined to be force radiation modes (frad-modes). An example is presented in which the acoustic power radiated by a simply-supported, baffled beam is reduced by using guidance provided by the structure’s force radiation modes. The results demonstrate that the force radiation modes can be used to guide the reduction of radiated acoustic power by changing the driving force location without the need to perform additional calculations or experiments.

Resilient bars can provide a low-cost, effective improvement to sound insulation performance. They are commonly used in timber-framed floor/ceiling assemblies in North America and Europe. Resilient bars are often modelled as springs isolating the two connected plates thereby forming a mass-spring-mass system. However, as a furring system of plates, resilient bars may modify the vibration energy distribution across a connected plate by acting as stiffeners. The authors investigate this issue by measuring acceleration levels at different locations relative to the fixing positions and thereby derive vibration waveforms for the connected plate in a small-scale structural simulation of a floor-ceiling system. The results were compared with timber-joist-ribbed, and timber-brander-ribbed, structures. The vibration modes of a suspended plate were also measured for comparative purposes. The results indicated that resilient bars did not perform as stiffeners whereas joists and timber branders did effectively stiffen their connected plates. Resilient bars neither forced orthotropic plate behaviour at low frequencies, nor separated the plate into sub-plates at higher frequencies. Resilient-bar-ribbed plates may also differ from independent plates. The modal behaviour of resilient-bar-ribbed plates is more complex and their effect on modal density and radiation efficiency are worthy of further research.

Microperforated panels (MPPs) can provide wide-band absorption without fibrous and porous materials and are recognized as next-generation absorption materials. Although the fundamental absorbing mechanism of an MPP absorber is Helmholtz-resonance absorption, sound-induced vibration of an MPP itself can affects the absorption characteristics. There have been some studies considering the effects of the sound-induced vibration and there even is a proposal to widen the absorption bandwidth by positively utilizing the vibration of an MPP itself. On the other hand, in a previous study, the relationship between MPP absorbers and panel-type absorbers was investigated with infinite theory. However, the relationship between Helmholtz-resonance absorption and panel-type absorption in finite flexible MPP absorbers has not been clarified. Herein, from the viewpoint of an absorption-characteristics transition with the perforation ratio, the relationship between Helmholtz-resonance absorption and panel-type absorption including the effects of eigen-mode vibrations of the panel is theoretically and experimentally investigated. The analytical model considers a finite flexible MPP supported in a circular duct, and the predicted data for the absorption coefficient under normal incidence is validated by an experiment using an acoustic tube. From this investigation, it is found that panel-type absorption due to eigen-mode vibrations of the panel occurs independently from Helmholtz-resonance absorption, while panel-type absorption due to a mass–spring resonance of a panel and a back cavity has a trade-off relationship with Helmholtz-resonance absorption with respect to the perforation ratio.

In this work the effect of two different bridge configurations on the vibrations of the top plate of a classical guitar is presented. Experimental harmonic analysis and visualization techniques, in addition to detailed damped simulations using the finite element method, were used to obtain mobility functions and operating deflection shapes of a top plate. The mobility functions were obtained in the following sequence. First the mobility functions were obtained on the top plate without a bridge attached. Then a bridge was glued to the top plate and new measurements were made. Finally the already attached bridge was cross-cut in situ without detaching it from the top plate, and the measurements were repeated. Those specific designs were chosen on the grounds of simplicity of construction both experimentally and in FEM simulations (no particular preference for those designs is implied). The assembly and the specific design of the bridge have shown to have considerable influence on the response of the top plate regarding the mode shapes above 300 Hz. Depending on the geometry of the bridge, its deflections can either be comparable to the maximum deflections of the top plate or can have amplitudes so small that the bridge effectively creates a nodal zone on the plate vibrations. This suggests that the shape, the stiffness, and the mass properties of the bridge may play a role in the sound quality of the instrument.

Orthogonal contributors to a global error represent a very efficient design method in terms of both sensing and control of noise radiation. In practice the price of a sensing system will be determined by the number of errors it must resolve. Therefore predicting the most efficient way of measuring radiation power is an important problem. Recently work has compared sensing the number of vibration modes to the number of orthogonal contributors to radiated power. The required number of vibration modes was based on the proximity of the structural mode resonance frequency and the excitation frequency. While ultimately this technique will result in a valid estimate of radiated power, it is shown here that the number of structural modes can be minimized by first considering orthogonal radiators based on structural mode amplitudes. Two disturbance cases are considered: a point force and an even disturbance coupling to each structural mode. Also, under these conditions the practicality of estimating the number of orthogonal radiators when it is assumed that each contributor is equal in amplitude is examined. Finally in an attempt to optimism the number of signals to be sensed, a variable error margin for the estimate of power, based on the ratio of the sound power at each frequency to the maximum peak in the considered frequency range is proposed and analyzed.

This paper describes methods used for determining the characteristic acoustic modes and frequencies of a liquid–propellant rocket–motor combustion chamber and effects of radial baffles on the chamber’s acoustic field. A multi-point sensing experimental setup, including stationary and moving sensors, was used to measure characteristic frequencies and mode shapes of a combustion chamber. A new technique based on the comparison of signal phase angles from stationary sensors to that of a moving sensor was used to map complex characteristic mode shapes of a combustor. A three-dimensional Helmholtz acoustic solver was also developed using an efficient finite volume approach for complex geometries to simulate the acoustic field inside a combustor. Using this approach the effects of the convergent section of the nozzle and the number of radial baffles on the chamber’s dominant acoustic modes with no mean flow were investigated. We have shown that the classical reduction of characteristic frequency of tangential modes caused by radial baffles is due to longitudinalization of tangential modes and is a function of the blade length and weakly dependent on the number of blades. Also, conjugate spinning modes are decoupled and do not spin in any baffled combustor, independent of the number of blades. On the other hand the converging nozzle section of a combustion chamber modifies pure longitudinal modes in the radial direction and pure tangential modes in the longitudinal direction. Existence of some mixed tangential–longitudinal modes in a combustor is dependent on the ratio of the nozzle throat diameter to the combustor head plate diameter.

In this study, the three-dimensional finite element frequency domain acoustical analysis is used to determine the modal shapes of cylindrical foam with a rigid backing and subjected to a unit normal incidence impulsive sound pressure loading while placed in the impedance tube. The acoustic results predicted for the foam are validated by data from the two-microphone acoustic measurements, and good agreement between the measured and predicted acoustic results is observed. The mode shapes of the incident face of the foam at a low frequency, resonant and anti-resonant frequencies as well as the frequency that occurring the peak loss modulus are illustrated. It is found that the modal behaviors of the cylindrical foam are dominated by the fluid, although the acoustic properties of the cylindrical foam are also influenced by the circumferential edge constraints and the modal movements of the solid skeleton.

This paper presents acoustic measurements obtained by mechanically exciting vibratory modes in single-crystalline silicon wafers with hairline periphery cracks of different type and location. The data presented shows a dependence of natural frequencies, peak amplitudes and damping levels of four audio vibration modes in the frequency range up to 1000 Hz on crack type and crack location. Data from defective wafers exhibit lower natural frequencies, higher damping levels, and lower peak amplitudes. The results suggest an impact test method may be useful for solar cell crack detection and quality control.

In this paper, an analytical approach for nonlinear forced vibration of a multi-degree-of-freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the free-interface vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a nine-degree-of-freedom system is considered, in which all spring have cubic type nonlinearity. As a result, it is shown that when there are no rigid modes in components, the compliance by the proposed method agrees very well with the exact one even if the lower vibration modes of components are only adopted. The other hand, in the case with rigid modes in components, the compliance has a little error compared with the exact result. It is recognized that the method proposed is very effective in the case without rigid modes in components for the actual application.

The acoustic radiation behavior of a plate with a distributed mass loading is studied. A set of in vacuo normal modes or fluid-loaded undamped normal modes are used for modal analysis of the acoustic radiation from a plate in air or in water. Modal radiation efficiency, modal volume displacement, modal input energy and sound power level are computed to show the effects of size and location of the mass loading on the acoustic radiation of the plate. It is observed that the acoustic radiation behavior of a mode in both cases will have relatively larger changes if the mass loading is placed on an antinode of the mode shape or the mass loading is more concentrated. The acoustic radiation behavior of a mode and the radiated power of the plate in water have less change than those in air with the same mass loading due to the added mass of the water, especially for the first few modes.

The measurement of radial directional natural frequency and damping ratio in a vehicle tire has been studied. Natural frequencies and damping ratios in the radial direction of various tires, from passenger car tires to truck bus tires, are reported. The radial direction modal parameters of tires subjected to different levels of inflation pressure, have been determined by using a frequency response function method. To obtain the theoretical natural frequency and mode shape, the plane vibration of a tire has been modeled as though it were that of a circular beam. By using the Tielking method that is based on Hamilton’s principle, theoretical results have been determined by considering the rotational velocity, tangential and radial stiffness, radial directional velocity and tension force which is due to tire inflation pressure. The results show that experimental conditions can be considered as the parameters that shift the natural frequency and damping ratio.

A generic matched-field processor is used to analyze vocalizations and “gunshot” type sounds from North Atlantic right whales (Eubalaena glacialis), recorded on a horizontal array deployed on the seafloor in the Bay of Fundy, Canada. The replicas are computed using a normal mode propagation model based on an effective depth approximation due to Zhang and Tindle for obtaining the modes. The code is computationally efficient, though restricted to constant sound-speed water over an attenuating fluid or solid layered bottom. Error estimates for frequencies within the right whale vocalization range were obtained with a test source deployed at known locations.

The relationship between the dominant mode of the submerged thin cylindrical shell and the flexural wave velocity is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, it is difficult to estimate the dominant mode, especially if two or more vibration modes are involved. To estimate the dominant mode of a thin shell in vacuo, the concept of “modified bending stiffness” has been introduced. In this paper, the concept of modified bending stiffness is extended to estimate the dominant mode of a submerged thin cylindrical shell. The dominant mode of a submerged thin cylindrical shell is theoretically discriminated from the other mode based on the smallness of the modified bending stiffness of the submerged shell. The validity of our theory is confirmed by a good agreement between theoretical and experimental results on flexural wave velocity.

For free vibrations of polar orthotropic plate, simple approximate closed form solutions for mode shapes and its natural frequencies were obtained using the Rayleigh–Ritz method. Coordinate function satisfying the natural boundary conditions and the predetermined coefficients was adapted, which results in compact expressions and enables to readily calculate symmetric and nonsymmetric natural frequencies for arbitrary values of the elastic constants. The derived formulation can be used in designing of circular plates such as wood disk, which are naturally endowed with material orthotropy as well as fiber reinforced composite materials. The model can easily be used for the evaluation of parametric studies on dynamic behaviors and nondestructive methods during the initial design process.

A theoretical analysis for the free vibration of simply supported buried pipes has been investigated using the wave propagation approach. The pipe modeled as a thin cylindrical shell of linear homogeneous isotropic elastic material buried in a linear isotropic homogeneous elastic medium of infinite extent. The vibrations of the pipe are examined by using Fluggle shell equation. The natural frequencies are obtained for the pipes surrounded by vacuo or elastic medium. The results are compared with those available in the literature and agreement is found with them. It is found that the free vibration frequency of the pipe does not appear for some of the axial or circular vibration modes and the real natural frequencies of the pipe are significantly dependent on the rigidity of the surrounding medium.

Complementing earlier studies on tenor and double second steel pans, vibrational mode shapes have been studied in cello and bass pans by two well-known pan makers. Normal modes are determined from operating deflection shapes recorded by means of electronic TV holography. Vibrational modes of the various note areas are designated by the number of radial and circumferential nodal lines. Tuners generally tune one mode an octave above the fundamental and, if possible, a third mode is tuned either a 12th or two octaves above the fundamental. Modal shapes in the skirts correspond to standing bending waves propagating around the circumference of the pan. The contributions of skirt vibrations and air cavity resonances to the observed sound spectra are small.

This paper describes the vibration responses of a cement viaduct model under impulsive force excitation. The frequencies and mode shapes of resonances can control magnitude of the structure-borne noise radiation. A steel hammer is used to excite the cement viaduct model at the centre and at the supporting edge position of the cross-section separately in order to acquire the vibration responses and mode shape data. From such data the global mode and local modes of the cement viaduct model are identified. It is shown that the edge of section supported by the web may have low impedance in the vertical direction. The results of analysis using a Finite Element Method confirmed the experimental findings of the cross-sectional modes of the cement viaduct model. The findings suggested that the vibrations of local modes are of two types: (1) Centre mode – the centre of top panel can move but the edge is fixed. (2) Edge (web) mode – the centre of panel is fixed but the edge (supported by web) can move.

This paper presents a technique for blade damage detection based on spatial wavelet analysis. The wavelet transform is used to analyze spatially distributed signals (e.g. mode shape) of cracked thick rotating blades. First, a finite element model is applied to the vibration of a thick rotating blade with a single edge crack. The effects of transverse shear deformation and rotatory inertia are taken into account. Then the mode shapes of the cracked rotating blade are analyzed by wavelet transformation. The effects of crack locations and sizes on the wavelet coefficients are studied. It is found that the distributions of the wavelet coefficients can identify the crack position of the rotating blades by showing a peak at the position of the crack. Then the signals are analyzed by wavelet transform. It is found that the distributions of the wavelet coefficients can identify the crack position. Assumed measurement errors are added to n th mode shape for evaluating the effect of measurement errors on the capability of detecting crack position. The moving average method is used to process the data with assumed measurement errors. The crack positions can also be identified when there exist assumed measurement errors.

This paper presents a technique for structure damage detection based on spatial wavelet analysis. Many damage detection methods require modal properties before and after damage. This method only needs the spatially distributed signals (e.g. the displacements or mode shapes) of the rectangular plate after damage. First, spatially distributed signals of the rectangular plate with damage are obtained by finite element method. The damaged region is represented as the elements with reduced stiffness. Then these spatially distributed signals are analyzed by wavelet transformation. It is observed that distributions of the wavelet coefficients can identify the damage position of rectangular plate by showing a peak at the position of the damage. It is also demonstrated that this method is very sensitivity to the damage size.