Structural-acoustic Coupling Research Articles

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Exact acoustical analysis of vibrating rectangular plates with two opposite edges simply supported via Mindlin plate theory

This study investigates acoustic radiation of rectangular Mindlin plates in different combinations of classical boundary conditions. A set of exact close-form sound pressure equations are given for the first time using the so-called Mindlin plate theory (a first-order shear deformation theory) for the plates having two opposite edges that are simply supported. The other two edges may be given any possible combination of free, simply-supported and clamped boundary conditions. It is assumed that no fluid loading occurs on the plate structure. In order to study the transverse vibration of moderately thick rectangular plates, the dimensionless equations of motion are derived based on the Mindlin plate theory. Structural–acoustic coupling is implemented for vibrating plate models. The radiation field of a vibrating plate with a specified distribution of velocity on the surface can be computed using the Rayleigh integral approach. The acoustic pressure distribution of the radiator is analytically obtained in its far field. To reveal the excellent accuracy of our exact acoustical solution, a comparison is first made with the existing data. Additionally, a few 3-D plots of the directivity pattern and their corresponding contour plots are illustrated for moderately thick rectangular plates with different boundary conditions. Finally, the influence of six possible combinations of boundary conditions, aspect ratios and thickness to length ratios on the sound pressure, frequency and critical distance parameters are examined and discussed in detail.

Prediction of the basilar membrane response to low-intensity acoustic stimulation using a mathematical model of the cochlea.

In the mammalian cochlea, the basilar membrane separates two fluid‐filled ducts and vibrates in response to acoustic stimulation. In vivo measurements of a viable basilar membrane show that the membrane is very sensitive to low‐level acoustic stimulation. A finite element model of the cochlea has been developed that explicitly couples the fluid, mechanical, and electrical domains of the cochlea. The proper function of the cochlea relies critically on structural acoustic coupling as well as electromechanical active control. The high sensitivity of the basilar membrane to low‐intensity sounds is explained by the presence of somatic motility in outer hair cells. The outer hair cells convert electrical energy to mechanical energy, amplifying basilar membrane motion. Recent experiments show that the tips of the outer hair cells, the hair bundle, can also produce an active force at acoustic frequencies. Active force production by the hair bundle is included in the model to predict the effects of hair bundle motility on the basilar membrane vibrations. Our model allows us to answer important questions about the interplay of the various active forces in the cochlea; questions that are difficult to address by experiments alone.

606 実稼動状態における騒音低減のための感度解析

For considering countermeasure of the noise in vehicle cabin, structure-acoustic coupling analysis needs to be conducted. Conventionally, the input identification under operational condition has been the first step to tackle with the problem. However, the input identification is usually time-consuming and needs practical skills. This paper proposes a new sensitivity analysis for the noise reduction under operational condition without using input identification. The structure modification is investigated based on the operational response. The proposed method is applied to the mass-added structure modification. It is confirmed that the noise level decreases as it was predicted based on the proposed approach.

Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity

A theoretical study on the vibroacoustic performance of a rectangular double-panel partition clamp mounted in an infinite acoustic rigid baffle is presented. With the clamped boundary condition taken into account by the method of modal function, a double Fourier series solution to the dynamic response of the structure is obtained by employing the weighted residual method (i.e., the Galerkin method). The double series solution can be considered as the exact solution of the problem, as the structural and acoustic-structural coupling effects are fully accounted for and the solution converges numerically. The accuracy of the theoretical predictions is checked against existing experimental data, with good agreement achieved. The influence of several key parameters on the sound isolation capability of the double-panel configuration is then systematically studied, including panel dimensions, thickness of air cavity, elevation angle, and azimuth angle of incidence sound. The present method is suitable for double-panel systems of finite or infinite extent and is applicable for both low- and high-frequency ranges. With these merits, the proposed method compares favorably with a number of other approaches, e.g., finite element method, boundary element method, and statistical energy analysis method.

Coupled wavenumbers of structural acoustic waveguides: A unified asymptotic approach

In the literature, the coupled wavenumbers in flexible‐walled acoustic waveguides have been found mainly using numerical methods for a fixed set of parameters. These solutions, although useful, do not continuously track the coupled wavenumbers as the fluid‐loading parameter is varied from small to large values. Such a continuous tracking is possible by applying the asymptotic methods to the coupled dispersion relation. Analytical formulae for the coupled wavenumbers can also be found. In this work, we present a consistent, unified and physically insightful view of structural acoustic coupling in the context of a planar structural‐acoustic waveguide (with two different BCs), the axisymmetric and beam modes of a fluid‐filled circular cylindrical shell and finally a fluid‐filled elliptic cylindrical shell. In all the five cases, we use a single fluid‐structure‐coupling asymptotic parameter (ε). The regular perturbation method is used to solve the coupled dispersion relation for small and large values of ε. The circular and the elliptic cylinders necessitate the use of additional asymptotic parameters. A general trend in all systems is that a given wavenumber branch transits from a rigid‐walled solution to a pressure‐release solution with increasing ε. Also, the wavenumber curves veer where the earlier uncoupled wavenumbers intersected.

ANALYTICAL MODEL OF SOUND TRANSMISSION THROUGH ORTHOTROPIC DOUBLE WALLED CYLINDERICAL SHELLS

Due to the high levels of noise into the modern launchers, the structural-acoustic coupling problem is an important subject in the area of vibro-acoustic analysis. In this paper, analytical study is conducted on oblique plane wave incident upon a flexible orthotropic double-walled thin cylindrical shell to understand the characteristic of sound transmission. External and internal fluid media surround the shells and there is fluid (air) in the annular space between them. A uniform flow moves with a constant velocity in the external fluid medium. The wave equations represent the fluid media and the Sanders equations describe the motions of the two shells. On the internal and external shell surfaces, the equations of fluid-structure interaction are considered. An exact solution is obtained by solving the classical shell equations and acoustic wave equations simultaneously. As, the pressure and displacement terms are expressed in infinite series form, an iterative procedure is constructed in each frequency. T...

Acoustic optimisation design for suspension characteristics based on the method of dynamic subsystem modification

Based on the finite element technique on the structure-acoustic coupling analysis, a dynamic subsystem modification method for the acoustic-vibration characteristic of an elastic thin-walled cavity is introduced in this paper. It is directly applied to the dynamic modification of an automobile's passenger compartment and then supports the Noise, Vibration and Harshness (NVH) performance analysis on the suspension system. The design objective is minimising the sound pressure level of the interior noise of the passenger compartment and the design variables are the stiffness and the damping of suspension system. Finally, the effect of the optimisation design is validated through a calculating example.

Mechanisms of active control of sound transmission through a linked double-wall system into an acoustic cavity

The mechanism of active control on sound transmission through a mechanically linked double-wall structure into an acoustic cavity is investigated in this paper. Two control methods, i.e., structural control and acoustic control under two linkage cases (soft and hard) are investigated to analyze the effect of the links on the selection of control strategies and the corresponding control mechanisms. Simulations are performed to examine the dominant control mechanism (modal suppression or modal rearrangement) in different frequency ranges for each control case. The alteration in the structural-acoustic coupling is also analyzed so as to explain the mechanisms of sound attenuation. In addition, the dominance of the acoustic mode (0, 0, 0) in the energy transmission process as well as its use in designing a more effective sensor/actuator arrangement is discussed.

Vibration Fatigue of Centrifugal Fan Impeller Due to Structural-Acoustic Coupling and Its Prevention: A Case Study

Fatigue cracks from high cycle vibratory loading have developed in a centrifugal fan impeller after a relatively short period of operation. Based on vibration tests of the impeller and acoustic analysis of the internal spaces of the fan, structural-acoustic coupling with matching frequencies involving two-nodal diameter modes (structural and acoustic) was identified as the cause of the vibration problem. This paper gives a description of the problem and identifies available remedies for its elimination. Special attention is given in Case 1 to the acoustics of the system, where changes to the fan casing utilizing a decoupling acoustic chamber attached to the casing was investigated, and in Case 2, where changes needed to the structural characteristics of the impeller by utilizing a modified impeller with a substantially increased natural frequency (by 44%) of the two-nodal diameter vibratory mode shape were studied. Experimental tests confirmed that the structural-acoustic coupling and vibration were significantly reduced in Case 1 and were fully eliminated in Case 2.

The Analysis of Structural–Acoustic Coupling of an Irregular Enclosure Under the Excitation of Point Force and PVDF

The physical model of this paper is an irregular enclosure with double flexible plates. The primary source is the vibration of Plate A excited by a point force. The secondary source is the vibration of Plate B excited by a polyvinylidene fluoride (PVDF) actuator. First, the interaction of the PVDF actuator and a thin plate is analyzed and the distribution of strain and stress is gained. Based on the hypothesis of linear distribution of strain on two sections of the plate–film system, a formula is deduced to calculate the rate of the strain distribution. Then an experiment is proposed to test the sound pressure response in an irregular enclosure under the excitation of the PVDF actuator. Second, the theoretical formulas of the mode contributions of the two plates and the cavity are deduced. Then the formulas are converted into compact matrix equations. Thus the expression of sound response of one point in the enclosure is gained under the excitation of both the primary and the secondary sources. Based on these results, the sound pressure square is taken as the control aim function. At last the optimized curves of control voltage and control phase are achieved.

Active noise control of a mechanically linked double panel system coupled with an acoustic enclosure

Active control of sound transmission through a mechanically linked double-wall structure into an acoustic enclosure is investigated in this paper. Based on a fully coupled vibro-acoustic model, the effect of mechanical links on the selection of control strategies is studied by examining (a) cavity control using acoustic sources inside the air gap and (b) structural control using structural actuators between the two panels. The relationship between the transmission path and the control strategies is explored. Numerical results show that cavity control can provide good noise attenuation for soft links when acoustic transmitting path dominates, while either structural or cavity controls can be used with the increase of stiffness of links depending on the frequency range of interest. For each case, the dominant control mechanism is examined and the alteration in the structural–acoustic coupling is analyzed to explain the mechanisms of attenuation. The effect of the acoustic mode (0,0,0) on active control of energy transmission is also discussed, giving guidance to choosing the appropriate control arrangement to ensure the maximum control performance.

Acoustic-Structural Resonances of Thin-Walled Structure—Gas Systems

This paper summarizes a theoretical study, which is a natural continuation of approximately 50 years of research in the field of acoustoelasticity. Recently, the researchers’ interest has been directed towards considering compressible fluid in contact with thin walled structures as it was found that the acoustic-structural coupling significantly changes the dynamic behavior of the system. Despite the interesting findings the main results still need additional, numerical, or experimental verification. The present work is intended to cast more light on the acoustic-structure coupling of light fluid-shell systems using a numerical approach, namely 3-D finite element (FE) modeling. Two different acoustoelastic systems are considered. The first system is a thin circular cylindrical shell containing light fluid in a coaxial annular duct and the second system is a thin-walled vehicle passenger compartment interacting with the enclosed cavity. Both systems are studied using ANSYS finite element code. The modeling involved shell finite elements for the structure and 3-D acoustic elements for the cavity. The 3-D FE modal analysis used produced results visualizing the complex picture of acoustic-structure coupling. It was confirmed that (1) in both fluid-elastic systems the strongest acoustic-structural coupling exists if the resonances of uncoupled acoustic and mechanical systems are close and (2) the nature of the acoustic-structural coupling is identical in the two cases studied. However, it was found that strong coupling between the thin-walled structure and the acoustic cavity exists in the vicinity of any uncoupled acoustic resonance. Thus, the coupled properties of the systems were found to be dominated by the uncoupled acoustic resonances. As the focus of this study is on the mode shapes of vibration, it was found that coupled acoustic-structure modes of vibration exist in the neighborhood of an uncoupled acoustic resonance, which means that the coupled system manifests a specific type of energy exchange. These modes were termed coupled “combined” modes to differentiate from the coupled component responses. It was also found that the coupled “combined” modes are clustered around a rigid-walled cavity mode, and any acoustic-structure resonance of a given group involves this particular uncoupled acoustic mode. In conclusion, it is shown that the acoustic-structure interaction causes the appearance of coupled “combined” modes not existing in the shell in vacuo or rigid-walled acoustic spectrum. It was found also that the subsystems preserve their capability of independent vibration responses, i.e., the response at the component modes is believed to be strong at their uncoupled frequencies.

ACTIVE STRUCTURE ACOUSTIC CONTROL WITHIN IRREGULAR ENCLOSURE BASED ON ANALYTICAL METHOD

A new analytical method for acoustic-structure coupled problem within an irregular enclosure, which has both inner sound source and exterior force exciting, is developed based on a method called covering domain method. The method is not only more accurate and faster than numerical method, such as FEM/BEM, but also can be used to solve acoustic-structure coupled problems within any irregular enclosure in a convenient way, which is impossible for the traditional analytical method. The model for active structure acoustic control (ASAC) system of an irregular enclosure based on the method above is founded, and then the optimized actuators outputs are given, which is the key step for ASAC system design. Then the method is applied to a car-like-cavity and it is found that the simulation result is quite good and shows us this new general analytical method for solving active structure acoustic control problem within an irregular enclosure considering acoustic-structure coupling is quite effective and fit for any irregular enclosure.

Vibrations and stability of a flexible disk rotating in a gas-filled enclosure—Part 1: Theoretical study

The vibrations and linear stability of a flexible disk rotating at sub- and supercritical speeds, and coupled to the acoustic oscillations of the surrounding fluid are investigated theoretically. The surrounding fluid is contained in a cylindrical enclosure. The coupled gyroscopic system equations are formulated using a Kirchhoff plate model for the disk, and the wave equation for the compressible fluid. The formulation includes systematically the effects of geometric perturbations such as radial clearances and asymmetric disk positioning, as well as bulk rotating fluid flows driven by fluid viscosity and disk rotation. A rigorous spatial discretization of this coupled gyroscopic system leads to a singular generalized non-Hermitian eigenvalue problem for which a special computational treatment is presented. The underlying physics of acoustic–structure coupling in the presence of these effects is complex—acoustic oscillations of the fluid above and below the disk couple through disk vibrations and through the radial clearance, while the bulk fluid rotation splits the acoustic modes into forward and backward traveling waves. Flutter instabilities arising from acoustic–structure mode coalescence and various damping mechanisms are discussed. The predictions reveal significant influences of radial clearance, asymmetric disk positioning, and bulk fluid rotation on the vibration and acoustic characteristics of the system that are likely to be observed in experiments, and in practical applications such as in CD/DVD drives and hard disk drives.

New Analytical Method for Modeling Active Structure Acoustic Control System within an Irregular Enclosure

A new analytical method for the acoustic-structure coupled problem within an irregular enclosure, which has both inner sound sources, and exterior forces exciting it, was developed based on a method called the covering domain method. The method is not only more accurate and faster than numerical methods, such as FEM/BEM, but also can be used to solve acoustic-structure coupled problems within any irregular enclosure in a convenient way, that are impossible for the traditional analytical method. The model for, the active structure acoustic control (ASAC) system of an irregular enclosure based on the method above was founded, and then the optimized actuators outputs were given, which is the key step for ASAC system design. Then the method was applied to a car-like-cavity and it was found that the simulation result is quite good and shows us this new general analytical method for solving active structure acoustic control problems within an irregular enclosure considering acoustic-structure coupling to be quite effective and fit for any irregular enclosure.

Structural-Acoustic Coupling Analysis of Two Cavities Connected by Boundary Structures and Small Holes

In some passenger vehicles, unexpected acoustic modes in the low-frequency range may be observed that cannot be explained by the conventional vibro-acoustic coupling analysis. It is because these methods only use the dynamic characteristics of a vehicle structure and its compartment cavity. However, some small holes or gaps existing at the boundaries between the compartment cavity and the trunk cavity of the vehicles change the modal characteristics of a coupled system. In this paper, a new analytical method is presented to investigate the structural-acoustic coupling characteristics of two cavities connected by small holes and in-between boundary structures. Small holes are modeled as an equivalent mass-spring-damper system in the analysis. A theoretical formulation for vibro-acoustic characteristics of this system is made, and the modal expansion method is used to obtain eigenvalues and their mode shapes. The validity of the proposed method is successfully examined by comparing the results of the analytical predictions with those of experiments.

구조-음향 연성현상을 갖는 방사 방향을 가질 수 있는 방사체 설계방법

This paper presents a design method for the structural-acoustic coupled radiator that can emit sound in the desired direction. A coupled system that has a finite space and a semi-infinite space separated by two flexible walls and an opening is considered. An objective function is selected to maximize radiation power on a main axis and minimize a side lobe level. To get initial values, prediction of a pressure distribution on field points and radiation pattern of the structural-acoustic coupling system is shown at a coupled-resonant frequency. Three different optimization methods are adapted to design the coupled radiator. Pressure and intensity distribution of the designed radiator is presented.

The analysis of structural-acoustic coupling of an enclosure using Green’s function method

Currently researchers expect to control the internal noise of an enclosure by controlling the relative structural vibration. The method is called ANC (Active Noise Control). Sound pressure response and velocity response of the structure are two significant factors to evaluate the performance of the ANC. But previous researches have to depend on a three-dimensional model with regular shape. Based on the Green’s function theorem this paper proposed two formulas to describe the contributions of acoustic modes and structural modes. These two formulas are the essential basis for the analysis of structural-acoustic coupling of an enclosure. From them compact matrix formulas are deduced and a numerical simulation method is presented to calculate the responses of sound pressure and velocity. The numerical simulation method is verified by comparing the numerical result with the theoretical one based on a regular model. And the application of the method in an irregular model shows this method can be used to analyze any model with arbitrary shape.

Effects of sound radiation on Sabine absorption coefficient of modally-reactive panels

A modally-reactive panel in a room absorbs and radiates sound at the same time when it is excited acoustically by the enclosed sound field. The absorption of sound occurs when only part of the incident sound is reflected by the panel, but when the entire panel vibrates, the radiation of sound is also produced. In this paper, Statistical Energy Analysis (SEA) is used to establish a relationship between the acoustic-structural coupling of the panel with the sound field and the Sabine absorption coefficient of the panel. It is shown that the coefficient does not only consist of the sound absorption by the panel from the room but also, the sound radiation from the vibrating panel back into the room. Computational and experimental examples are presented for different acoustical properties of the panel and the sound field to illustrate the extent of influence of the sound radiation on the coefficient. The results provide a basic understanding of the conditions in both cases where the sound radiation has significant effects and negligible effects on the determination of the Sabine absorption coefficient of modally-reactive panels in rooms.