Vibro-acoustic Coupling Research Articles

Electro-mechanical vibro-acoustic characteristics of submerged functionally graded piezoelectric plates with general boundary conditions

The present paper focuses on studying the underwater electro-mechanical vibro-acoustic characteristics of functionally graded piezoelectric material (FGPM) plates with general boundary conditions. For this purpose, the collocation points method is firstly developed to handle vibro-acoustic coupling, which can directly calculate the virtual work of secondary sound pressure via an easy double integral, without pre-simplifying the complex quadruple integral. The proposed FGPM plate model is established in the framework of first-order shear deformation theory (FSDT) and second type constitutive equations of piezoelectric materials, and the macroscopically inhomogeneous electro-mechanical properties are considered by means of Voigt model. The multi-physical fields including electric, mechanical and acoustic fields are uniformly extended in Chebyshev polynomials. Meanwhile, penalty function method is introduced to satisfy the arbitrary mechanical and electric constraints. All energy formulations are processed by Rayleigh-Ritz procedure and a standard governing equation is finally derived. Based on the proposed unified model, the convergence and accuracy for solving vibration and acoustic radiation of FGPM plates are validated firstly. Additionally, the influence of some key parameters on underwater vibro-acoustic characteristics of FGPM plates is fully examined. The results of this paper may provide a reference for future application of FGPM-based smart structures.

Topology optimization of single and double panels for improved sound insulation in specific frequency bands

Single and double panels are commonly employed in noise control, e.g., as partitioning elements between rooms and to enclose noisy machines. In presence of narrowband disturbances, related for example to rotating machines, further improvements in sound insulation can be obtained by properly distributing the material within the area of the panels. This allows maximizing the sound Transmission Loss (TL) in the frequency band of interest by controlling structural resonances and antiresonances. In order to achieve this goal, in this work, we apply numerical topology optimization to find the optimal material thickness distribution for single and double panels. In the iterative design process, single panels are schematized through a simple mechanical Finite Element (FE) model, while double panels are modelled considering the vibroacoustic coupling between the two mechanical plates and the internal acoustic air cavity. The sound insulation properties of the designed solution are evaluated by TL computations through hybrid Finite Element-Statistical Energy Analysis (FE-SEA) simulations. The method is applied targeting different frequency bands in the audible range and focusing on practically relevant design cases, such as single and double PMMA and glazing panels.

Vibro-acoustic coupling characteristics of the microperforated panel with local resonators

This paper provides a unified approach to evaluate the sound absorption performance of the metamaterial microperforated panel (MMPP) with additional local resonators under elastic boundaries. The elastic boundary conditions can be realized by setting the stiffness of restrained spring at the edges as a specific value. The vibration equations of the metamaterial panel (MP) are derived by combining the Spectral Geometry method with the Rayleigh Ritz method, and the acoustic electrical analogy method is used to solve the absorption coefficient considering the vibro-acoustic coupling. The program developed by these methods can be used to study the vibro-acoustic coupling model of the MMPP with various parameters under various boundaries. To validate the accuracy of the present method, a structure-acoustic simulation model is established, and a good agreement is achieved between the theoretical method and the finite element method. A comprehensive parametric analysis is performed to obtain the optimum suppression performance of sound absorption and the variation of the absorption coefficients has been explained justifiably in detail. The results demonstrate that additional local resonators can improve the absorption performance of the microperforated panel, and the absorption band can be appropriately broadened by reducing the spring stiffness or increasing mass ratio. This paper provides a better sound absorption prediction for the practical application of MMPP under complex conditions.

Vibration and Sound Radiation of Cylindrical Shell Covered with a Skin Made of Micro Floating Raft Arrays Excited by Turbulence

To reduce the vibration and sound radiation of underwater cylindrical shells, a skin composed of micro floating raft arrays and a compliant wall is proposed in this paper. A vibroacoustic coupling model of a finite cylindrical shell covered with this skin for the case of turbulence excitation is established based on the shell theories of Donnell. The model is solved with the modal superposition method to investigate the effects of the structural parameters of micro floating raft elements on the performance of reducing vibration and sound radiation of the cylindrical shell of this skin. The results indicate that increasing the stiffness ratio, damping ratio, mass ratio, or decreasing the interval between micro floating raft elements can improve the vibration and sound radiation reduction performance of this skin over the frequency range 0~2000 Hz. Moreover, the mean quadratic velocity level and sound radiation power level of the finite cylindrical shell with this skin can be reduced by 12.00 dB and 9.65 dB respectively compared to the finite cylindrical shell with homogeneous viscoelastic coating in the frequency range from 0~2000 Hz, implying a favorable performance of this skin for reducing the vibration and sound radiation of cylindrical shells.

Numerical Analysis of Combustion Chamber from Vibro-acoustic Coupling Characteristics Point of View

Numerical Analysis of Combustion Chamber from Vibro-acoustic Coupling Characteristics Point of View

Analytical model of vibro-acoustic coupling between the membrane loaded with concentrated masses and the acoustic cavity

In this paper, sound radiation and sound transmission characteristics of a membrane-cavity system loaded with concentrated masses are analyzed. The Fourier cosine series function with additional terms is used as the mode function of membrane to model the single membrane structure, which is suitable for arbitrary boundary conditions. The concentrated masses are regarded as the concentrated mass points without considering their sizes, and the coupling structure of membrane and mass blocks is constructed. The structure-sound field fully coupled model is also constructed by using the energy principle and Rayleigh–Ritz method. Several numerical examples computed by finite element method are used for verification. The influence of the added mass blocks on the membrane modes and acoustic properties of the coupling system is discussed, including membrane parameters, mass block arrangement, quantity and mass, etc. Also, the mass blocks are dispersed for analysis. Results show that dispersing the mass can significantly increase the frequency of the coupling mode between the membrane and concentrated masses and better suppress the vibration. But increasing dispersion points does not further enhance vibration suppression. Instead, it expands the area where the membrane vibrates violently.

A fast direct solver for non-intrusive reduced order modeling of vibroacoustic problems

This paper proposes a fast model order reduction method for large-scale three-dimensional vibro-acoustic coupling problems, which proceeds in three perspectives. Firstly, part of the coupling matrices is neglected and another part of the coupling matrices is treated as the partial right-hand side of the Schur complement of the corresponding subsystem in order to implement model reduction quickly. Secondly, the proposed fast method does not require the use of the underlying complex-valued and dense boundary element full-order model for the construction of a global orthonormal basis in the offline phase. Rather, its sparse approximation is exploited, which benefits from the consistent amplitude decay property of the kernel functions. This way it can be regarded as a non-intrusive method. Lastly, in addition to structural loads, acoustic loads, such as the load from incident waves impinging on the flexible structure from the outside, can be handled as well. Application of this solution method to the frequency sweep analyses of coupled structural acoustic systems, i.e. simple sphere and complex geometrical model submerged in an infinite fluid with the number of degrees of freedom ranging from hundreds of thousands up to millions, shows the improved computational efficiency and reduced memory requirement as compared to the brute force approach based on the direct evaluation of original high-dimensional models and also the previous acceleration scheme.

Sound transmission loss of a novel acoustic metamaterial sandwich panel: Theory and experiment

A novel acoustic metamaterial (AMM) sandwich panel with enhanced sound transmission loss (STL) is proposed and designed by periodically distributing the local resonators in the stiffened core. The vibro-acoustic coupling is considered by the continuity of velocity at the fluid–structure interfaces. The effective dynamic mass density method is used to investigate the influences of the local resonators on the reinforced STL of the sandwich panel. The space harmonic expansion method and the virtual work principle are applied to derive the dynamic equations. An acoustic experiment is carried out and compared with the theoretical result. Experimental and theoretical results show that the STL curve has a peak near the objective frequency of the local resonator. The vibro-acoustic behaviors are further investigated using the finite element method (FEM). The peaks and dips in the STL curves are explained by the vibration modes and stress distributions obtained by the FEM. The proposed AMM sandwich panel possesses improved sound insulation performance around the mass-air-mass resonance frequency. For specific working conditions, the present method can be used to improve the STL of sandwich plates by adding resonators.

Accelerated dispersion curve calculations for periodic vibro-acoustic structures

Over the years, metamaterials have shown their potential in a wide range of different disciplines, e.g. optics, electromagnetics, dynamics etc. Metamaterials are, often periodic, engineered structures made of conventional materials but which exhibit properties not encountered in nature. In the field of noise and vibration, metamaterials have received increasing interest since they can obtain frequency ranges of high noise and vibration attenuation, called stop bands. Their performance is often investigated by means of dispersion curves, which are calculated based on a single unit cell and assuming a structure of infinite periodic extent. Nowadays, the attenuation of acoustic and structural waves is commonly tackled as two separate problems, whereby either acoustic or structural dispersion curves are used. Recently, vibro-acoustic unit cell designs have come to the fore which can exhibit appealing characteristics, such as simultaneous structural and acoustic stop bands. To consider the vibro-acoustic coupling in these unit cell designs during the performance predictions, vibro-acoustic dispersion curve calculations are thus required. However, these computations are typically cumbersome to perform due to the associated high computational cost and therefore, often, uncoupled dispersion curves are used during the performance assessment. Although several unit cell model order reduction approaches have recently been proposed to accelerate the dispersion curve computations, such as the Bloch mode synthesis (BMS) and Generalized Bloch mode synthesis (GBMS), they are not readily applicable to vibro-acoustic unit cells. To accelerate vibro-acoustic dispersion curve calculations, this work extends the BMS and GBMS techniques towards 2D and 3D periodic vibro-acoustic systems. To balance accuracy versus speed, the extended BMS reduction basis is constructed using a split set of vibro-acoustic coupled modes, while the extended GBMS reduction basis uses the uncoupled modes. Several verification cases demonstrate that strongly accelerated vibro-acoustic dispersion curve computations are achieved whereby the vibro-acoustic coupling inside the unit cell is accurately accounted for.

Analysis on Vibroacoustic Fatigue Life of Empennage in a Hypersonic Vehicle

In this study, the fatigue life prediction in hypersonic vehicle noise environment is researched under the structural vibration caused by the engine jet noise and the aerodynamic noise. A finite element analysis model is first established, and then natural frequency and vibration mode are obtained. According to the modal analysis, the vibroacoustic coupling calculation is finished in the dynamic analysis software. Modal participation factor, modal displacement, and the power spectral density of the stress response on the coupled surface are acquired. The finite element, border component, and vibrating stress analytical techniques are also employed in this research to predict the acoustical fatigue performance of the tail fins of a specific type of spacecraft. On the basis of vibration fatigue theory, identified material S–N curve, and linear cumulative damage theory, the Dirlik model in the frequency domain method for vibration fatigue is used to predict the fatigue life of empennage. According to the characteristics of the acoustic load, effects of the load characteristics, and damping ratios on the fatigue conditions, the design of the antifatigue design is put forward.

Improved mode acceleration-based vibroacoustic coupling analysis of functionally graded shell under random excitation

This paper focuses on the vibroacoustic response of functionally graded material (FGM) shell structures under stationary random excitations. An eight-node finite element model of FGM shells is developed, which is valid for both flat and curved shells of FGM. Then, the finite element formulation of the acoustic-structural coupled system for FGM shells under random excitation is established. It is shown that the commonly used combined method of the pseudo excitation method (PEM) and mode displacement method (MDM) in previous work is highly efficient for stochastic dynamics problems, but its accuracy is reduced by the modal truncation error. To remedy this, the combined method of PEM and the conventional mode acceleration method (MAM) is an effective alternative, but not applicable to the coupled acoustic-structural system due to its singular stiffness matrix. To circumvent this, an efficient and accurate method integrating the PEM and the improved MAM (IMAM) is proposed for the vibroacoustic coupling analysis of FGM shell structures under stationary random excitation. Numerical examples are given to verify the effectiveness of the proposed method and to explore the random vibroacoustic properties of the FGM shells with different power-law distributions.

Low frequency noise control in duct based on locally resonant membrane with attached resonators

In this paper, locally resonant membrane with attached resonators is introduced to duct system to achieve good noise control effect especially in low frequency range. A rigorous analytical model based on modal expansion method is developed to investigate the vibroacoustic coupling characteristic of proposed duct-membrane-resonator system. The corresponding theoretical results show a good agreement with numerical simulation. The velocity distribution, sound transmission loss curve, and the mechanism behind are discussed and explained deeply. It is found that the attached resonators on the membrane can lead to new transmission loss peak which is related to but not exactly equal to the resonance frequency of attached resonator itself. Correspondence between zero equivalent density mass and transmission loss peak is achieved at the non-antisymmetric modes. Compared to single resonator, multi-resonators system can realize more transmission loss peaks for better sound transmission effect. In principle, ultra-low frequency noise reduction and arbitrarily adjustable frequency can be achieved by changing the frequency, position, and number of exerted resonators, which provide a new approach for duct noise control.

Vibro-Acoustic Analysis of Rectangular Plate-Cavity Parallelepiped Coupling System Embedded with 2D Acoustic Black Holes

An acoustic black hole (ABH) has the ability to concentrate and manipulate flexural waves, which can be used for structural vibration suppression and noise attenuation. In this paper, a 2D ABH rectangular plate is designed and a 2D ABH plate-cavity coupling system is constructed using the 2D ABH plate and five rectangular elastic plates of uniform thickness. Series of vibro-acoustic FEM models of the plate-cavity parallelepiped coupling system embedded with 2D ABHs are established, and the vibro-acoustic coupling simulation is conducted to analyze the effects of ABHs on the coupling modes, vibro-acoustic coupling characteristics, and mechanism of ABHs and the damping layer. It is shown that at most frequencies in the range of 3600~5000 Hz, the damping 2D ABH plate-cavity parallelepiped coupling system can significantly suppress the sound pressure and greatly reduce the peak values. It is also found that the significant reduction of the participation factor of the acoustic modes within the 100th order is the main mechanism for the obvious suppression of the sound pressure in the damping ABH plate-cavity coupling system at 3701 Hz. Finally, an experimental platform of vibro-acoustic measurement of the 2D ABH coupling system is constructed, and the accuracy of the vibro-acoustic FEM models of the 2D ABH coupling systems established in this paper and the numerical simulation calculation are verified by the vibro-acoustic measurement experiment.

Interval Analysis of Vibro-Acoustic Systems by the Enclosing Interval Finite-Element Method

Traditional interval analysis methods for interior vibro-acoustic system with uncertain-but-bounded parameters are based on interval perturbation theory. However, the solution sets by traditional interval finite-element methods are intrinsically not capable of reflecting the actual bounds of results, due to the non-conservative approximation for neglecting the high-order terms of both Taylor and Neumann series. In order to cope with this problem, this paper introduces the concept of unimodal components from structural mechanics to factorize the uncertainties, and a new enclosing interval-finite element method (enclosing-IFEM) is proposed to predict the uncertain vibro-acoustic response. In the enclosing-IFEM, the global matrix is assembled with the mixed-nodal-element strategy (MNE), which is different from the element-by-element assembly strategy. Thus, the vibro-acoustic coupling equation can be transformed into an iterative enclosure formula, and it avoids conflicts between the Lagrange multiplier matrix and the coupling sub-block matrix. The focus of this research is to reduce the overestimation caused by dependency phenomenon in the result of the enclosing-IFEM, therefore, both Rump’s and Neumaier–Pownuk methods are analyzed in residual convergence. Furthermore, taking the results of the Monte Carlo approach and other interval finite-element methods as the cross-references, both the efficiency and accuracy of the enclosing-IFEM are examined through two numerical validation examples.

Vibro-Acoustic Energy Transmission Analysis of the Acoustic Cavity with Multiple Partial Partitions

The general dynamic characteristics of the acoustic cavity with multiple partial partitions are presented in this thesis. A theoretical model has been developed for predictions, and several configurations are analyzed. To describe the apertures on the interface of subcavities, the virtual air panel assumption is introduced into the improved Fourier series system. The governing equations of the coupling system are derived by using the energy principle. The results obtained with the proposed model are firstly compared with the numerical calculations based on the finite element method (FEM). Subsequently, a configuration made up from a rigid cavity partitioned by a partial steel panel has been specifically built, and the forced responses of the coupling system have been measured for comparison and model validation. The present results are excellent over most of the studied frequency range. Furthermore, the visualizations of the interior sound intensity field of the acoustic cavity with three partial partitions under different frequencies are researched to illustrate the energy transmission paths and vibro-acoustic coupling mechanism of the complicated system. The obtained results are believed to be helpful in the optimal design of the vibro-acoustic coupling system with optimal sound insulation capacity.

Thermoacoustic modal instability and its suppression with locally resonant flexible membranes

Thermoacoustic oscillation and instability are a common occurrence in many industrial problems. Investigations on the interplay among different types of modes, their evolution process and coupling with add-on control devices are of vital importance to guide the development of proper control strategies. Using a linear heat release n-τ model inside a duct, these issues are investigated in this paper based on a fully coupled energy-based model. Studies allow the classification and quantification of different types of eigen-modes, as well as their stability and controllability features. Using flush-mounted flexible membranes over the duct wall, possible suppressions of unstable modes and the underlying control mechanisms are revealed with particular focus on cases involving small time delay and interaction indices. Numerical analyses show that thermoacoustic instability of the system can be controlled via creating strong vibro-acoustic coupling, via two different physical processes for acoustic and intrinsic modes. For the former, the acoustic modal pressure distribution should be positively altered in the vicinity of the heat source to create a favorable pressure state scenario, in agreement with Rayleigh criterion. For the latter, control is achieved indirectly through a proper alteration of the nearby acoustic modes, thus affecting their coupling with the targeted intrinsic mode. In both cases, a successful suppression of the thermoacoustic modal instability can be materialized through a proper adjustment of the physical parameters of the membranes and their installation locations.

Optimization of Noise Transfer Path Based on the Composite Panel Acoustic and Modal Contribution Analysis

The noise of a cab directly affects the comfort and labor efficiency of the operators. The optimization of the structure-borne transmission path can obviously reduce the cab noise. The method of panel acoustic contribution analysis (PACA) is used to reduce structure noise. However, most studies only consider the panel acoustic contribution of a single frequency, without considering the contribution of major frequencies synthesis to confirm the optimized panels. In this paper, a novel method is proposed based on composite panel acoustic and modal contribution analysis and noise transfer path optimization in a vibro-acoustic model. First, the finite element model (FEM) and the acoustic model are established. Based on the acoustic transfer vector (ATV) method, a composite panel acoustic contribution analysis method is proposed to identify the panels affecting the noise of the field point. Combined with the modal acoustic contribution of the modal acoustic transfer vector (MATV) method, the noise field point is confirmed in the area which has the most significant influence. Second, the optimization algorithm NLOPT which is a nonlinear optimization is applied to design the areas. The noise transfer path optimization with vibroacoustic coupling response can quickly determine the optimal thickness of the panels and reduce low-frequency noise. The effectiveness of the proposed method is applied and verified in an excavator cab. The sound pressure level (SPL) the driver’s right ear (DRE) decreased obviously. The acoustic analysis of the composite panel acoustic contribution and modal acoustic contribution can more accurately recognize an optimized area than the traditional PACA. This method can be applied in the optimization of the structure-borne transmission path for construction machinery cab and vehicle body.

Vibro-acoustic modelling of the box structural–acoustic coupling system

The eigenmodes and vibro-acoustic responses for the box structural–acoustic coupling system composed of a box structure and an acoustic cavity are predicted using the energy principle and improved Fourier series. The improved Fourier series are adopted to describe the vibrations displacements of the box structure built up by six elastically coupled rectangular plates and the sound pressure in the cavity. The improved coupling energies suitable for the box structure having coordinate systems in different directions are presented to deal with the coupling problem of multi plates. The vibro-acoustic coupling energies in the establishment of the energy functions are composed of the work produced by the interaction between the acoustic space and the six elastically rectangular plates composing box structure. The eigenmodes of the coupled system are derived by employing the Rayleight Ritz method against the energy funcitions for the box structural–acoustic coupling system. The reliability of the presented model is verified by the good agreement of the eigenfrequencies and vibro-acoustic responses predicted by theoretical method and finite element method.

Effect of modeling sidewalls on tire vibration and noise

Low-noise tire design demands the potent model, which regards accessible parameters in the design process before manufacturing a tire. Unlike most previous analytical models that integrated tire treadband with sidewalls with an assumption of identical properties, this research segregates them. The separation clarifies the effects of each tire part on vibration and noise individually, which has not been presented in previous publications and is noteworthy in design. The model is developed considering three connected plates, describing treadband and sidewalls, on an elastic foundation derived from vibro-acoustic coupling inside the tire. Natural frequencies are determined by the Galerkin method using modes shapes satisfying all boundary conditions. The vibration response of a tire rolling on the road is then formulated utilizing Green’s function and convolution integral. Eventually, vibrational tire noise is calculated by the boundary element method. Comparing the proposed model with the repeatedly used integrated plate model has indicated the dissimilarity of treadband and sidewall responses with a difference of 1.4 dB(A) in total noise level. Moreover, implemented parametric study based on a small central composite design has revealed their parameters’ distinct influences on generated noise. For instance, increment in treadband thickness reduces sound level, while decreasing sidewall thickness effectively leads to noise reduction. So, the proposed model is worth employing instead of the previous overused integrated model to predict and reduce tire noise.

Acoustic absorption of a metamaterial panel: Mechanism, boundary effect and experimental demonstration

The present paper investigates absorption of a metamaterial panel composed of a flexible micro-perforated panel attached periodically with local resonators. It gains good agreement between the results of the theoretical prediction and finite element simulation for the metamaterial panel while considering the vibroacoustic coupling between the sound excitation and the plate vibration. Both theoretical and finite element simulation results show that the local resonator can tune the acoustic surface impedance at desired frequency. The boundary effect of the metamaterial panel under the simply supported or clamped condition at all four edges is investigated. It shows that new absorption peak can be acquired differently under various boundary conditions. The absorption mechanism is further revealed by the displacement pattern and the surface impedance. Finally, a sample of four-edge clamped metamaterial panel is designed and fabricated. The experiment and simulation results validate the theoretical prediction.