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A theory is proposed to study the vibrations of homogenous isotropic circular cylindrical shells based on a developed plate vibration theory. By proposing a novel distribution of the shear stress and strain across the thickness of the shell, the arguments are adjusted such that the transverse shear strains and stresses equal zero at the shell surfaces. Due to the existing curvature in the circumferential direction, the defined shear stress and strain distributions consider a change in the position of the neutral plane toward the center of curvature. In the presented Two-Separated Lateral Displacement (TSLD) theory, the lateral displacement is defined by two bending and shear parts to provide an analytical model, referred to as the four-variable refined plate theory. The similarity to classical theory and involving only four unknowns are significant features of the introduced theory. The TSLD theory is verified against the available data in the literature. It is shown that the provided stress and stress distributions lead to more accurate results, especially in moderately thick cylinders. The proposed theory is remarkably more precise than classical shell theory and First-order Shear Deformation Theory (FSDT). Results of the TSLD theory are as accurate as the Higher-Order Shear Deformation Theory (HOST12) for the higher frequency parameters and more thick shells, while the TSLD theory implementation is much simpler than the HOST12.

Tri-stable magneto-piezoelastic oscillators exhibit superior performance in terms of broadband resonance frequency and lower excitation threshold, compared to linear and bi-stable systems. Furthermore, inclusion of magnets renders them applicable, tunable, and simple designs. However, the potential of this oscillators for the purpose of simultaneous vibration suppression and energy harvesting has not been investigated. This study aims to investigate simultaneous energy harvesting and vibration isolation through a tri-stable magneto-piezoelastic absorber (TMPA). The absorber comprises a bimorph cantilever beam carrying a magnetic tip mass and two external magnets. The interplay between magnets generates a nonlinear restoring force in the TMPA structure. This absorber is attached to a host vibrating beam, which is under a transient or periodic forcing, in order to reduce its vibrations and harvest electrical energy. The nonlinear magneto-electromechanical equations governing the coupled system are obtained by employing the Hamilton's principle, Euler-Bernoulli beam theory, and a recently proposed magnetic force relationship. First, the mechanisms of tri-stability formation are investigated via bifurcation diagrams. Next the potency of the TMPA in the transient excitation scenario is examined. Furthermore, the performance of the TMPA in the presence of the periodic excitation with different forcing levels is investigated. Specifically, frequency and time domain analyses are carried out to characterize the response of the system and efficiency of the absorber when TMPA performs periodic in-well, aperiodic inter-well and periodic inter-well oscillations. In addition, to provide a better insight regarding the TMPA performance, the kinetic energies, harvested power, and dissipated power for the region of strongly modulated response are also studied. Moreover, the efficacy of the TMPA in periodic snap-through oscillations is examined by the means of the harmonic balance method in conjunction with pseudo-arclength continuation scheme. Finally, the results disclosed that the proposed tri-stable absorber outperforms a linear absorber in vibration annihilation and energy harvesting.

A viscoelastic model is proposed in this approach to determine the sound transmission loss coefficient of a sandwich shell system with double curvature. The structure is composed of a double-walled composite shell subjected to a viscoelastic core. Investigating the efficient impresses of rotary inertia and shear deformation, vibration equations of both outer and inner shells are extracted within the framework of shear deformation shallow shell theory. Besides, the Zener mathematical model is used for viscoelastic material, which is based on a spring connected in series with a parallel mixture of spring and dashpot. This model presents the dynamic response in the whole frequency domain at which shear modulus and bulk complex modulus are frequency dependent. Since the performed studies on the sound transmission loss of this kind of structures are insignificant, the outcomes of plate models with a viscoelastic core are used to provide a reliable sound transmission loss comparison. The results show that the applied strategy can improve the acoustic characteristics of the system at high frequencies compared to that of a single-layer one with the same mass. This issue is more highlighted while the thickness of the viscoelastic layer enhances, which confirms the positive performance of the viscoelastic materials in this range of frequency, particularly in the resonant frequency. In addition to the curvature effect on acoustic features, the vibration response of the system is configured based on various frequencies and materials.

This paper investigates simultaneous vibration suppression and energy harvesting through a continuous dynamic vibration absorber (DVA) with piezoelectric coupling, both numerically and analytically. The proposed system is composed of a simply supported host beam that is under a periodic external forcing or transient excitation in the form of an initial condition. Besides, a DVA is attached to the host beam. First, the governing electromechanical equations of the coupled system are derived. Next, convergence analyses are performed to find the effects of the considering higher modes of the host and absorber beam. Furthermore, the frequency response curves of the mechanical and electrical responses are obtained. It is observed that the DVA can effectively annihilate the host structure vibrations, up to 98.5%, and at the same time harvest considerable levels of voltage/power. Moreover, comprehensive investigations on the role of various mechanical and electrical parameters on the system responses are carried out. To validate the numerical results, an analytical solution is provided and a great agreement between these solution schemes is observed. Also, the dynamics of the considered system under an initial condition is inspected. Finally, the effects of the PZT layers in vibration isolation performance are studied. Results divulged that, upon the proper tuning of the mechanical and electrical parameters, the proposed DVA can significantly scavenge energy and mitigate vibrations.

In this approach, acoustic response of a Magneto-electro-elasticity (MEE) shell structure is determined using three-dimensional (3D) theory of elasticity. The structure is composed of a curved shel...

This article is provided to investigate the free vibrational behaviors accompanied by buckling characteristics of carbon nanotube-reinforced conical shells via the Haar wavelet technique. For a better performance in the thermal environments, materials used in the structure obey the temperature-dependent relations. On the other hand, carbon nanotubes are embedded across the thickness uniformly or functionally. Using Hamilton’s principle through the first-order shear deformation theory yields governing equations. Both dynamic and stability states are evaluated in the vicinity of equilibrium state and are also derived with regard to initial thermal stresses that are obtained via linear membrane technique in static analysis. The obtained partial differential equations are converted into ordinary ones with the aid of separating variable technique. Subsequently, the Haar wavelet approach is used to discretize the equations meridionally and transform them into new algebraic ones. Capability of this approach in calculation of frequencies with only a few numbers of the collocation points is demonstrated. Finally, to verify the integrity and precision of the proposed approach, some comparison studies are made with those of relevant results in the literature primarily. Thereafter, some effective parameters such as the geometry of nanotube, different boundary conditions, temperatures, and material properties are studied.

Both natural and synthetic fibers do not perform well at low frequencies and are also subjected to erosion, moisture, fire, etc., when used as an interior finish of room walls. To overcome these pr...

This study collects all of the existent papers in the field of acoustic transmission across multilayered plate constructions. Herewith, a comprehensive source is proposed wherein approximately 410 references are reviewed and described from the first [Formula: see text] to [Formula: see text]. In the first part, in addition to the presentation of a complete explanation about the importance of the acoustic analysis of these structures, appropriate formulations are also provided. Furthermore, an overview of the thematic correspondent is carried out. Since the type of material used in these constructions can be very important in sound insulation, the significance of this subject is remarked. The papers are then classified based on their acoustic excitation fields containing plane wave, diffuse, random, and point source. After analyzing the research approaches according to different environmental properties, the articles are ordered based on their boundaries as finite and infinite. To present reliable outcomes, it is necessary to investigate a proper theory proportional to the structure’s thickness. Herewith, this issue is also discussed in detail. The review is also expanded to focus on the different vibroacoustic solutions. Before concluding remarks, the authors' research works are presented wherein either optimization algorithms or control techniques improve the acoustic performance of these structures.

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

In this contribution, a review study is established in order to gather, classify and organize all of the previous researches on the sound insulation characteristics of plate structures with span a period from 1967 to nowadays. Accordingly, more than 200 articles in the area of acoustic performance of these structures are rolled up and reviewed. To achieve this end, in the first step, all of the existence papers are categorized and classified based on the thematic correspondent. Herewith, not only some appropriate descriptions about the importance of the issue are given but also a series of basic equations and generalities in this field are developed. The paper is then conducted to focus on the various theories in order to present the reliable results according to thickness of structures. In this regard, different theories including classical, shear deformation and three-dimensional are highlighted. To extend the review, a comprehensive explanation is provided with emphasis on the type of materials such as composite, isotropic and functionally graded. It is useful to note that sandwich plate structures with their subdivisions are also set in this group. Consequently, the structures are organized according to their boundary conditions. Besides, the importance of type of incident field is inspected, too. Subsequently, in order to remark the methods employed by the researchers, the works are reviewed based on their solution techniques. Before concluding remarks, the remained papers are classified on the basis of various procedures such as optimization and control of sound transmission through plate structures.

This article presents the numerical results for acoustic transmission through relatively thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical shells. The vibration ...

This paper deals with analyzing the nonlinear vibration of an isotropic cracked plate interacting with an air cavity. A part-through surface crack with variable orientations and positions is considered and modeled using the modified line spring model. In the first step, based on the Von Karman theory, the governing equation of the nonlinear vibration related to the cracked plate–cavity is presented. Then, by employing the Euler equation along with the Galerkin method, the coupling effect between the fluid–solid media inside the enclosure is eliminated. In the next step, the variational iteration method (VIM) is introduced as an appropriate method for nonlinear analysis of the mentioned system. To this end, the convergence of the nonlinear coupled natural frequencies with high precision is proved by performing four iterations of VIM. Finally, the effect of the length, angle, and position corresponding to the crack as well as the cavity depth on the frequency ratio is inspected for various boundary conditions by plotting three and four-dimensional backbone curves. It is revealed that the crack angle is the most effective parameter on the frequency ratio.

Fluid-conveying micro/Nano structures are key tools in MEMS and NEMS applications especially for drug delivery systems to attack a specific tumor like cancer cells. Vibrational characteristics of such tools play a crucial role in delivering efficient and reliable performance in various applications. As a result, vibration and instability control of such systems is of great importance. Vibration and instability response of magnetostrictive sandwich cantilever fluid-conveying micro-pipes is investigated in this paper utilizing smart magnetostrictive layers as actuators. Euler–Bernoulli beam model together with modified couple stress theory (MCST) are used to model the problem. As main properties of these smart layers, magnetic intensity effect, velocity feedback gain and thermal effects are taken into account in the modeling. The governing equation is extracted employing Hamilton’s principle. Extended Galerkin procedure is applied to discretize the governing equation and obtain the eigenvalue problem which is solved straightforwardly to reach the eigenvalues. Afterwards, eigenvalue diagrams are studied to analyze the vibrational characteristics and possible instabilities (flutter and bifurcation) occurring in first three modes of the system. Throughout this analysis, the role of various intrinsic properties of the magnetostrictive layers on the critical flow velocity and frequency is studied in detail. The numerical results show a good ability for the used smart layers to control the instability of fluid-conveying micro-pipes. Therefore, these sandwich structures may be helpful for achieving a novel design for such systems.

This paper presents an analytical model to embed porous materials in a finite cylindrical shell in order to obtain the sound transmission loss coefficient. Although the circumferential modes are considered only for calculating the amount of the transmitted noise through an infinitely long cylinder, the present study employs the longitudinal modes in addition to circumferential ones to analyze the vibroacoustic performance of a simply supported cylinder subjected to the porous core based on the first order shear deformation theory. To achieve this goal, the structure is immersed in a fluid and excited by an acoustic wave. In addition, the acoustic pressures and the displacements are developed in the form of double Fourier series. Since these series consist of infinite modes, it is essential to terminate this process by considering adequate modes. Hence, the convergence checking algorithm is employed in the form of some three-dimensional configurations with respect to length, frequency and radius. Afterwards, some figures are plotted to confirm the accuracy of the present formulation. In these configurations, the obtained sound transmission loss from the present study is compared with that of the infinite one. It is shown that by increasing the length of the structure, the results are approached to sound transmission loss of the infinite shells. Moreover, a new approach is proposed to show the transverse displacement of a finite poroelastic cylinder at different frequencies. Based on the outcomes, it is found that by enhancing the length of the poroelastic cylinder, the amount of the transmitted sound into the structure is reduced at the high frequency domain. However, the sound insulation property of the structure is improved at the low frequency region when the radius of the shell is decreased.

The present approach considers hybrid control strategy to reduce the amount of transmitted sound through a multilayered doubly curved sandwich shell equipped with piezoelectric layer and shunt circuit. The construction is composed of some piezoelectric actuator and sensor layers as an active controller as well as resistance–inductance shunt circuit as passive controller. In addition, a layer made of isotropic material is also sandwiched as a core. Firstly, in order to obtain the electromechanical equations of curved shell integrated with piezoelectric layers, Hamilton’s principle, and shear deformation shallow shell theory are employed. After presenting the sound transmission loss of structure, the reliability of the formulation is checked by the aid of previous outcomes. In the following, the piezoelectric layers coupled with shunt circuit are employed to inspect the influence of these patches on the control of transmitted sound through structure. The results indicate that the shunt circuit is able to enhance the sound transmission loss at resonant frequency with no need source of energy. Since in designing the engineering structures, the transmitted noise control is important especially in the resonant frequency, the influence of using several parallel shunt circuits with each piezoelectric layer is also examined. It is shown that increment of the number of parallel shunt circuits implies substantial reduction of transmitted sound to the structure in the resonant frequency. Finally, the solution process is followed to study the effect of active control on the acoustic transmission. Then, it is found that employing the simultaneous active and passive controllers not only cause to reduce the transmitted noise in the resonant frequency but also make to improve the behavior of sound transmission loss in entire range of frequency.

This paper reviews the most of previous works through vibroacoustic performance of shell structures in past years (1957–2019). The major end is especially placed to collate the researches carried out in the area of power transmission through shell structures during the last 60 years. For this purpose, a series of categories are first highlighted in order to classify the issues that should be searched. The review is then directed with emphasis on the kinds of shells with different geometries containing cylindrical and doubly curved shells. Later on, not only a popular discussion is proposed to model the acoustic behavior of shells based on the different theories (classical, shear deformation and three-dimensional) but also a perfect explanation is provided wherein the importance of modeling the structures according to the different materials is revealed. To extend the review, various boundary conditions (finite and infinite) are also investigated. Besides, the further effects of external environments as fluid and thermal are inspected. Since the type of incident field can be impressive on the sound insulation specification of these shells, the structure is characterized based on the various acoustic excitations involving plane wave and point source incidences. Furthermore, some descriptions on the solution procedures (analytical, experimental and numerical) are also given. As a result, the review is centralized through other matters such as control and optimization techniques in order to improve the vibroacoustic behavior of shell structures.

The main goal of this paper is to investigate the size-dependent nonlinear vibration and stability response of fluid-conveying sandwich micro-pipes exploiting magnetorheological elastomer (MRE) as a smart core. Considering the geometrical nonlinearity, based on von-Karman assumption, Euler–Bernoulli theory is employed for mathematical formulation of the problem. Additionally, modified couple stress theory (MCST) is utilized as a size-dependent theory to reach an accurate model. Kerwin assumption is taken into account, and Hamiltonian’s approach is hired to derive the coupled and nonlinear governing equations and boundary conditions of the system. For solution procedure, differential quadrature method (DQM) is used to discretize the governing equations and corresponding boundary conditions. Thereafter, the obtained algebraic nonlinear equations and boundary conditions are solved numerically to acquire the nonlinear eigenvalues of the system which could be analyzed to discuss the stability and critical flow velocity of the system. In numerical analysis, a detailed examination is conducted to elucidate the exact influences of the main intrinsic characteristics of MRE core (i.e., magnetic intensity and MRE core thickness) on vibrational response of the system. Accordingly, the main effects of the MRE layer on vibrational properties including frequency, loss factor, critical flow velocity and stability region for both cantilever and clamped–clamped pipes are investigated. The results reveal the substantial effect of the MRE core on the vibrational characteristics and stability of the system. The boosting effect of the MRE core layer on the stability of the system was disclosed. The results declare that, in addition to the magnetic intensity as a controlling parameter, the MRE core thickness is another important factor in vibration and stability characteristics of the system. Totally, the research reveals that the fabulous properties of the MRE layers could be considered and exploited in designing the fluid-conveying micro-pipes to obtain an efficient, smart and adaptive system response.

In this study, a robust controller against the uncertainties in piezoelectric patches including sensor and actuator is designed based on sliding mode method to control the radiated sound from cylindrical shells. Accordingly, in order to extract and discretize the dynamic equations of a smart cylinder equipped with piezoelectric patches, the Hamilton’s principle and the Rayleigh-Ritz method are, respectively, used . The radiated sound is estimated by the Kirchhoff-Helmholtz integral and the acoustic structural sensing method. Furthermore, an innovative approach is proposed on sliding mode control to model system uncertainties and design robust control signals against these disturbances. Using effective control signals for each mode is the applied methodology for establishing independent sliding surfaces. In fact, it is attempted to relate between actuator matrix determinant and system control ability in generating the efficient control signals and error reduction due to actuators uncertainties. By the aid of this relation, optimization of the actuators position according to the genetic algorithm is implemented. The obtained results show that by optimizing the actuators position not only the appropriate performance of the system in controlling the radiated sound from the structure is enhanced but also the essential control voltage for each actuator is significantly decreased.

The present research aims to analyze a piezoelectric energy harvester under simultaneous effects of two hard excitations. The system consists of a unimorph cantilever beam carrying a tip mass; excited by two simultaneous hard base accelerations. The governing distributed-parameters partial differential equations (PDEs) of motion are obtained based on Euler-Bernoulli beam assumption accounting for geometric nonlinearity. Galerkin scheme is exploited to discretize the PDEs into a set of nonlinear ordinary differential equations (ODEs). The convergence analysis is carried out to obtain the minimum required number of modes. To generalize the further results, the dimensionless forms of ODEs are obtained. Then, the approximate-analytical solutions are derived based on multiple scales method (MSM) for the case of simultaneous occurrence of superharmonic and combination resonances. Frequency response curves of the displacement and voltage are plotted. Moreover, the harvester response is studied for the case of primary resonance. The results disclose that, the level of the generated voltage and power are amplified when the superharmonic and combinations resonances coexist in the system response. Furthermore, the system dynamics are investigated in the time domain, showing good agreement with the frequency domain findings.

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.

Acoustical investigation of a thin plate having a part–through surface crack surrounded by an air enclosure is studied in this paper. The enclosure comprises five rigid walls and a flexible plate based on the Kirchhoff plate theory. It is also assumed that the crack is located at an arbitrary position and orientation with a specific length. Accordingly, partial differential equation related to the coupled cracked plate–cavity system is presented. In order for the partial differential equation (PDE) to be solved, firstly, the sound pressure inside the cavity is estimated by a suitable number of the plate modes. Then, the coupled PDE decomposes to some ordinary differential equations in the time-domain by employing the Galerkin method for three different boundary conditions. In addition, the linear natural frequencies are obtained in vacuo and coupled conditions for an uncracked plate and then, a similar procedure is performed for a cracked plate. Furthermore, comparing the results with available data in the literature shows the reliability and accuracy of the present work. Finally, the influences of the crack angle, crack length, crack position, and cavity depth on the natural frequencies are investigated.

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.

Fluid-conveying micro/nano tubes are key tools, which have great applications in biological devices and especially smart drug delivery in order to target the cancer cells. Furthermore, exploiting the smart materials and their combination with drug delivery systems may positively affect the instability control and improve the efficiency and adaptability of design. Recently a specific size-dependent behavior for piezoelectric materials, known as flexoelectric effect, has drawn a great deal of attention. It is proven that this effect, which is resulted by coupling between the strain field and electric polarization, is of significant importance in structures with nano dimensions. This paper is carried out to investigate the vibrations and instability analysis of fluid-conveying piezoelectric nanotubes on the basis of flexoelectricity approach. The fluid-conveying nanotubes made for drug delivery targets are commonly in contact with soft tissues, which could be modeled as a Kelvin-Voigt foundation. The nonlocal strain gradient theory (NSGT) constitutive relations are employed in order to model the problem. An appropriate electric potential distribution is determined using the Maxwell's equation and Gauss's law. The Euler-Bernoulli beam theory and slip boundary conditions are exploited to derive the governing fluid-structure interaction (FSI) equation, which contains flexoelectric and surface effect terms. Galerkin's principle is hired to discretize the equation leading to an eigenvalue problem. Afterwards, the obtained characteristic equation is solved straightforwardly to gain the eigenvalues. The instability of the nanotube is investigated throughout presenting the eigenvalue diagrams. Some illustrations are employed to analyze the effect of different involved parameters on the vibrations and instability behavior of the system. The reported results in the numerical section of the paper may be helpful to achieve an efficient and accurate design of fluid-conveying nanotubes.

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.

This paper aims to investigate the free vibrational analysis of the generally doubly-curved shells of revolution made of functionally graded (FG) materials and constrained with different boundary conditions by means of an efficient, convenient and explicit method based on the Haar wavelet discretization approach. The FG materials of the shell consist of a combination of ceramic and metal, which four parameter power-law distribution functions have chosen for modeling of the smoothly and gradually variation of the material properties in the thickness direction. The theoretical model of the shell is formulated by employing of the first-order shear deformation theory. The rotation and displacement components of each point of the shell are expanded in the form of product of the Haar wavelet series in meridional direction as well as trigonometric series in the circumferential direction. By adding the boundary condition equations to the main system of equations, the constants appeared from the integrating of the Haar wavelet series are satisfied. In addition, with solving the characteristic equation, the vibrational results including the natural frequencies and the corresponding mode shapes are achieved. Then, the present results have been compared with those available in the literature. The results indicate that this method has high accuracy, high reliability and also a higher convergence rate in attaining the frequencies of the FG doubly-curved shells of revolution. Also, the effects of the main parameters such as power-law exponent, geometrical parameters, material distribution profiles and different types of boundary conditions, on the vibrational behavior of the FG doubly-curved shells of revolution, are investigated. Finally, taking into account the effects of geometrical parameters and material distribution profiles, for FG doubly-curved shells of revolution with different boundary conditions such as classic, elastic restraints and their combination, a variety of new frequency studies are provided which can be considered as proof results for further researches in this field.

This paper is concerned with the vibration analysis of a rotating tapered axially functionally graded (AFG) nanobeam. The material properties of the nanobeam are assumed to vary along its length. Accordingly, Newtonian method is employed to derive the governing equation of the system considering Euler-Bernoulli beam assumptions. Also, the nonlocal elasticity theory (NET) is used in order to take the small scale effects into account in the modeling. In addition, the differential transformation method (DTM) is hired to solve the attained differential equation semi-analytically. Therefore, the obtained equations as well as boundary conditions are transformed into algebraic equations by the aid of DTM. Then, the characteristics equation can be solved to gain the non-dimensional frequencies of the system. After presenting the convergence and verification illustrations, some numerical results are discussed in detail to investigate the influences of various parameters namely nonlocal parameter, tapered ratio, angular velocity and FG index on the first three non-dimensional frequencies. As a principal result, it is disclosed that the nonlocal parameter shows both stiffness-hardening and stiffness-softening behavior in different bounds of the angular velocity. Totally, the numerical analysis reveals some important findings which are hoped to be used in efficient design of nano-structures benefited from the rotating nanobeams.

In this paper, thermal buckling and free vibration of orthogonally stiffened functionally graded truncated conical shells in thermal environment is investigated. Conical shell has been stiffened by...

This paper presents the fundamental problem of three-dimensional acoustic wave transmission through a sandwich structure with viscoelastic core excited by an obliquely plane wave. The structure consists of a functionally graded shell as an outer layer, an isotropic layer as an inner layer and also a viscoelastic core. This work considers Havriliak-Negami model for description of complex modulus of viscoelastic core. The Havriliak-Negami model is a new mathematical method for the simulation of polymeric relaxation behavior in the frequency domain. In this model, both of complex Young’s and shear moduli are frequency dependent. Moreover, considering the effective roles of shear deformation and rotary inertia, dynamic governing equations of the functionally graded cylinder, viscoelastic core and isotropic shell are derived within the frameworks of the three-dimensional theory of elasticity. Furthermore, analytical model of acoustic wave transmission based on transfer matrix method is composed of a set of fluid and structural equations which taking into account the frequency dependency of mechanical characterization for the viscoelastic core. A good agreement can be observed, comparing the present results with those of other authors. Besides, the results show that a double-walled cylinder with viscoelastic core has a better acoustic insulation in comparison with isotropic shell with the same mass. Contrary to elastic material, by thickening the viscoelastic layer, sound transmission loss decreases in mass-controlled region due to shear deformation and rotary inertia. It has been also proved that polymer with a larger loss factor has good performance in energy dissipation.

Corrugated structures are widely being used in industrial applications, which raises the demand for careful analysis of their behavior. To fill the gap for vibroacoustic characteristics, this paper focuses on proposing a model to investigate sound transmission through double-walled cylindrical shells with a circumferentially corrugated core. The structure is composed of outer and inner isotropic layers and a corrugated core. The outer layer is subjected to an oblige plane wave, and also a subsonic flow is traveling outside the double-walled shell. An equivalent method is applied to replace the corrugated core as axial, radial, and rotational springs with specific stiffness coefficients. The first-order shear deformation theory (FSDT) is applied to describe the behavior of isotropic shells. A considerable parametric study is established concerning both the incident wave and structural characteristics. The results show that the presence of the corrugated core improves sound transmission loss (STL) of the structure in the mass-controlled region, and it has a negative effect on STL in the coincidence-controlled region; therefore, using such a core for sound insulation depends on the desired frequency domain.

Bistable systems possess broadband characteristics and can have large-amplitude oscillations under low amplitude excitations. This work is aimed to investigate the potential of a bistable piezoelectric-based absorber (BPA) for the purpose of simultaneous energy harvesting and vibration suppression. The BPA composed of a cantilever beam with PZT layers and two permanent magnets. The interactions due to magnets generate bistability in the BPA. Furthermore, the absorber is connected to a main vibrating beam. The governing nonlinear equations are obtained using the Hamilton's principle and a recently developed magnetic force model. Next, numerical analyses in time and frequency domains are performed to characterize the BPA performance in various dynamical regimes. It is found that, the best performance occurs when the BPA exhibits chaotic inter-well oscillations, which lead to strongly modulated response (SMR). Furthermore, approximate-analytical investigations based on the complexification-averaging and multiple scales methods are carried out. Using these, the excitation threshold corresponding to SMR is obtained. The performance of the proposed BPA in terms of harvested power and dissipated energy are examined comprehensively. The results reveal that, the BPA efficiently suppresses the vibration and harvests power over a wide frequency band, and it outperforms a linear absorber and nonlinear energy sink.

Acoustic analysis of the four-sides simply supported doubly curved composite shell interlayered with porous material used in aerospace applications is considered based on Third order Shear Deformation Theory (TSDT). The focus is specifically placed on presenting the effect of boundaries on Sound Transmission Loss (STL) of the poroelastic structure. Then, the results are compared with those of infinite shell. In order to calculate the STL, the displacement and pressure terms are derived in the form of double Fourier series for a simply supported boundary condition doubly curved shell. A new approach is made to consider the number of modes for the finite composite structure treated with porous material. In addition, the simultaneous solution of the equations of porous and composite layers along with acoustic wave equations is performed. This process leads to obtain the unknown constants in all parts of the structure including upper and bottom composite shells as well as porous core which results in presenting the STL of the structure in the logarithmic scale. Since, the solution is provided in the form of modal infinite series which should be terminated at the sufficient modes, the convergence checking is prepared in 3D configurations with respect to various frequencies and shell dimensions to present the number of the appropriate modes for this process. Moreover, the results are validated with the aid of other researches including experimental as well as analytical models available in literature. Finally, some new results including Sound Pressure Level (SPL) in both of global view and contour map, transverse displacement configurations and the effects of various shell dimensions on STL, are presented for this finite structure.

This paper investigates a diffuse acoustic field to analyze the wave propagation on infinite doubly curved laminated composite shell sandwiching a porous material which is extensively used in aerospace structures. In fact, the main goal is to study the influence of embedded porous core on Sound Transmission Loss (STL) of the structure. Accordingly, Biot's theory is employed to model the poroelastic material which considers three types of wave propagation including two compression and one shear terms. In addition, Shear Deformation Shallow Shell Theory (SDSST) is applied to derive the wave propagation through double-walled laminated composite shell. Moreover, a numerical process is prepared to investigate a random incidence STL in a diffuse acoustic field which results in presenting the Limiting angle of incidence in which no incident wave is transmitted through structure. Then, in order to show the accuracy and the reliability of the present results, some comparisons are made between the achieved results and those of analytical as well as experimental results available in literature. Besides, the importance of using porous material as a core has been presented. Finally, some effective parameters have been studied in numerical results to inspect the insulation property of the current composite structure.

The present work optimizes Sound Transmission Loss (STL) and weight of double-walled composite cylinder with poroelastic foam employing multi-objective genetic algorithm by offering Variabl...

An analytical model is performed across the aerospace composite structure to interpret acoustic transmission of the infinitely long doubly curved shell considering the effect of mean flow with the aid of Higher-order Shear Deformation Theory (HSDT). Accordingly, the displacements are extended up to cubic order of thickness coordinate based on Third-order Shear Deformation Theory (TSDT) known as HSDT including no effect of shear correction factor. Consequently, in order to present the Sound Transmission Loss (STL) of the present model, the excitation of the structure with an oblique plane sound wave is set in order. However, the acoustic transmission is performed by incorporating the both of shell equations and acoustic wave equations, simultaneously. In the next step, the accuracy as well as the reliability of the present model is provided by comparing the achieved results with those available in literature. Moreover, the present results illustrate the importance of investigating TSDT due to clarifying the more precise outcomes. Finally, the importance of the present model is cleared as a result of improving the mechanical and sound insulation properties particularly in low frequency zone by illustrating the STL comparison between the current structure and those structures without any curvature.

The present work applies three-dimensional elasticity theory as well as extended full method based on Biot’s theory to inspect the effect of compressing porous material on sound transmission loss o...

Because of the modification in environmental conditions, thermal stresses may induce dynamic instability in a composite shell model. Therefore, according to the double Fourier series solution, an analytical strategy is proposed in this study for the first time to acoustically determine the vibration response of a doubly curved composite shell in a thermal environment . The main aim is to show the effect of thermal loads on sound transmission loss (STL). The motion equations of the structure integrated with thermal stresses are derived considering shear deformation shallow shell theory (SDSST) through Hamilton’s principle. Before verifying the outcomes, the convergence of the STL curve is also checked to prove that the obtained results are reliable. Parametric studies are performed to either show the temperature effect on acoustic characteristics or propose a 3D configuration of thermo-acoustic pressures through the system. Based on the temperature variations, it is found that there is an opposite trend between the increase of this term and the STL of structure. This issue also causes to move the dip point of the STL spectrum to lower frequencies. To manifest the fact of these behaviors, the natural frequency ratio against temperature rise is also plotted.

This paper investigates efficient simultaneous energy harvesting and vibration suppression utilizing a tunable bi-stable magneto-pieozelastic absorber (BMPA). The absorber comprises a bimorph cantilever beam exposed to a magnetic field. Furthermore, it is attached to a primary simply supported beam which is under an external excitation. The nonlinear magneto-electromechanical equations governing the coupled continuous system are derived utilizing the Hamilton's principle. First, the nonlinear magnetic force and its bifurcations are explored. Next, using numerical approaches, the efficacy of the absorber under a transient excitation from energy harnessing and vibration annihilation viewpoints is assessed. Furthermore, the efficiency of the BMPA in a steady-state harmonic excitation is investigated, both in time and frequency domains. Bifurcation diagrams disclosed that, based on magnets gap, the absorber performs periodic in-well low-amplitude oscillations, chaotic inter-well large-amplitude vibrations, or periodic high-amplitude motions. However, it is observed that in inter-well oscillations, chaotic strongly modulated response occurs and efficiency of the BMPA in vibration mitigation and energy harvesting markedly improves, compared to a linear absorber. Moreover, perfection rate examinations disclosed that when vibration suppression and energy harvesting are of the same importance, the bistable PZT absorber performance is 46.5% better than the corresponding linear absorber. Furthermore, when energy harvesting has priority, the BMPA performance is 158% higher than the linear absorber. Finally, harmonic balance method along with pseudo-arclength scheme are exploited to investigate the efficacy in large-amplitude inter-well scenario. It is illustrated that the system solutions are nonlinear and experience various cyclic fold and Hopf bifurcations. Further, the frequency response curves revealed that the BMPA decreases the host structure vibrations. Moreover, in this scenario, a considerable level of voltage is generated over a wide frequency range.

Effects of imperfect bonding on sound transmission across a double-walled cylinder with FGM-core are studied by using the three-dimensional theory of elasticity. Aluminum and zirconia are inner and outer shells respectively, whereas the FGM-core is sandwiched between these layers. A very thin adhesive epoxy interlayer was applied in order to bond the adjacent layers. The imperfect bonding (adhesive epoxy interlayer) is modeled by a linear spring model. Infinite values of stiffness of linear spring reveal that there are no interfaces between the adjacent layers. However, the interface tractions do not exist and the layers are completely deboned from each other due to zero values of these parameters. The linear spring model is incorporated into the global transfer matrix with the aid of suitable transfer matrices. The proposed model is used to calculate the effects of imperfect bonding on TL of multi-layered cylinder which excited by an external plane wave. The obtained results are compared with those of other researches recently published in the literature. Excellent agreement is observed for high stiffness of adhesive bond. The results have also illustrated the fact that the existence of imperfect interfaces leads to the enhancement of the TL of sandwich cylindrical shell. Moreover, low stiffness of interlaminar adhesive bonding has more positive effect on the TL enhancement, particularly in high frequency range. Finally, it can be concluded that at high frequencies the spring layer model with low stiffness cannot transmit the waves because of more fluctuations.