Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall

In this paper, a fully coupled vibro-acoustic model is developed to characterize the structural and acoustic coupling of a flexible panel backed by a rectangular-like cavity with a slight geometrical distortion, which is introduced through a tilted wall. The combined integro-modal approach is used to handle the acoustic pressure inside the irregular-shaped cavity. Based on the model proposed, the distortion effect on the vibro-acoustic behavior of the coupled system is investigated using the averaged sound pressure level inside the enclosure and the averaged quadratic velocity of the vibrating plate. Simulations are conducted to examine the distortion effect on acoustic natural frequencies, acoustic pressures and structural responses. Effects of the wall inclination on coupling coefficients are also assessed, and an index is proposed to quantify the degree of variation of coupling strength.     

Reduction of radiated exterior noise from the flexible vibrating plate of a rectangular enclosure using multi-channel active control

This study attempted to control the radiated exterior noise from a rectangular enclosure in which an internal plate vibrates by acoustic excitation and noise is thus radiated from that plate. Multi-channel active control was applied to reduce the vibration and external radiation of this enclosed plate. A piezoelectric ceramic was used as a distributed actuator for multiple mode control of the vibration and radiated noise in the acoustically excited plate. To maximize the effective control, an approach was proposed for attachment the piezoelectric actuator in the optimal location. The plate and internal acoustic space in the enclosure are coupled with each other. This will change dominant frequency characteristics of the plate and, thus, those of the externally radiated noise. Active noise control was accomplished using an accelerometer attached to the plate and a microphone placed adjacent to that plate as an error sensor under acoustic excitation of sine wave and white noise. It was found that the control of radiated external radiation noise requires a microphone as an error sensor, a sound pressure sensor due to vibration of the plate, differences in the dominant frequency of externally radiated noise, and complex vibration modes of the plate.     

Vibro-acoustic behaviour of laminated double glazing enclosing a viscothermal fluid cavity

This paper presents a new numerical model to investigate the vibro-acoustic behaviour of two laminated glass plates enclosing a thin viscothermal fluid cavity. The aim of this work is to develop an original five layer (two skins plies, two adhesive films and a core ply) laminated plate finite element by mixing Kirchhoff and Mindlin plate’s theory. The formulation is based on the theory that accounts for the transverse shear in the adhesive films and in the core. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of fluid and by taking into account the fluid-structure interaction. The discretization of the energy functional by finite element method gives after minimisation a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. Therefore, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system’s response. Then, the validation of the new laminate finite element model is achieved by comparing the sandwich plate results against data obtained from literature. Subsequently, predicted responses, such as the vibration transmissibility and the transmission loss of the coupled system, for a given laminated double glazing under an imposed homogeneous pressure are presented and discussed. Numerical results show the importance of both lamination and viscothermal fluid effects on double glazing vibro-acoustic behaviour.     

Fractional Green–Naghdi theory for thermoelectric MHD

ABSTRACT

In this work, we use the Green–Naghdi theory of thermomechanics of continua to derive a linear theory of MHD thermoelectric fluid with fractional order of heat transfer. This theory permits propagation of thermal waves at finite speed. The one-dimensional model of the theory is applied to Stokes’ flow of unsteady incompressible fluid due to a moving flat plate in the presence of both heat sources and a transverse magnetic field. The problem was solved using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. A numerical method based on a Fourier-series expansion is used for the inversion process. The thermoelectric effects with fractional parameter on the temperature and velocity fields are analyzed and discussed in detail with the aid of graphical illustrations.     

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Unsteady flows of two immiscible Maxwell fluids in a rectangular channel bounded by two moving parallel plates are studied. The fluid motion is generated by a time-dependent pressure gradient and by the translational motions of the channel walls in their planes. Analytical solutions for velocity and shear stress fields have been obtained by using the Laplace transform coupled with the finite sine-Fourier transform. These analytical solutions are new in the literature and the method developed in this paper can be generalized to unsteady flows of n-layers of immiscible fluids. By using the Laplace transform and classical method for ordinary differential equations, the second form of the Laplace transforms of velocity and shear stress are determined. For the numerical Laplace inversion, two accuracy numerical algorithms, namely the Talbot algorithm and the improved Talbot algorithm are used.     

Transient sloshing in half-full horizontal elliptical tanks under lateral excitation

A semi-analytical mathematical model is developed to study the transient liquid sloshing characteristics in half-full horizontal cylindrical containers of elliptical cross section subjected to arbitrary lateral external acceleration. The problem solution is achieved by employing the linear potential theory in conjunction with conformal mapping, resulting in linear systems of ordinary differential equations which are truncated and then solved numerically by implementing Laplace transform technique followed by Durbin's numerical inversion scheme. A ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of tank aspect ratio, excitation input time, and baffle configuration on the resultant sloshing characteristics are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained.     

Theory and calculation for acoustic radiation mode of weak coupled enclosure

Active structural acoustic control(ASAC)is an efficient method in acoustic radiation control of coupled enclosure.In the past research of ASAC,the concept of "acoustic radiation mode(ARM)of coupled enclosure"was proposed,which was a set of basis functions of structural mode amplitude.However,there was an incompatibility with the ARM definition in free space radiation case which was a set of basic functions of normal velocity or pressure on the vibrating surface.Also,there was severe inconvenience for application as structural modes were required while accurate and useful structural modes were difficult to be extracted in practice.To overcome these problems,by analogy to ARM theory of free space,the acoustic potential energy was expressed in quadratic form of normal velocity on coupling surface and ARM of coupled enclosure was redefined.Furthermore,theoretic derivation showed that ARM of coupled enclosure could be replaced simply by corresponding acoustic mode projection of enclosure when the coupling surface was discretized into equal size elements.Therefore,the ARM theory of coupled enclosure which was consistent with that of free space and convenient for application was formed.Finally,numerical calculation was performed and the results proved that the presented theory was very efficient in ARM calculation of coupled enclosure and ASAC.     

用拉普拉斯变换差分法求解试井分析中的一维渗流问题

结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.     

Active absorption to reduce the noise transmitted out of an enclosure

This paper investigates the potential of active absorbers for reducing low-frequency noise transmission through an enclosure. Active absorbers are intended to obtain a purely real prescribed impedance at the front face of a porous layer. This is achieved by an active control system which cancels the acoustic pressure at the rear face. The test bench was a simplified enclosure: a rigid-wall cavity coupled to a baffled elastic plate. The modeling of the system was based on an analytical modal approach. The purpose of this simulation was first to calculate the optimal impedance, providing maximal reduction in radiated power, and then to define a sub-optimal strategy for actual absorber production. Two 3-cell configurations were implemented on the test bench. Active control used a multichannel feedforward algorithm. In line with prediction, the absorbers provided a 5.5 dB overall reduction while covering only 2% of the cavity surface.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

A numerical study on the enhancement of heat transfer by pressure distributions in acoustic fields

The enhancement of heat transfer in a cavity was investigated in the absence of and in the presence of acoustic streaming induced by ultrasonic waves. The present study provides the experimental and numerical results of heat transfer in the acoustic fields. The enhancement of heat transfer was experimentally investigated in the presence of acoustic streaming and was compared with the profiles of acoustic pressure calculated by the numerical analysis. A coupled finite element-boundary element method (FE-BEM) was applied for a numerical analysis. Experimental and numerical studies clearly show that pressure variations are closely related to the enhancement of heat transfer in the acoustic fields.     

Identification of a dynamical model for an acoustic enclosure using the wavelet transform

This paper presents results of research work in the identification of a dynamical model for an acoustic enclosure, a duct with rectangular cross-section, closed ends, and side-mounted speaker enclosures. An acoustic enclosure is excited randomly and random decrement functions are built to convert the random responses to free acoustic responses. It is shown that the estimation of resonance frequencies is possible using the wavelet transform of the system’s free response. Using a particular form of the son wavelet function, results are improved compared to those obtained with the traditionally Morlet wavelet function. An optimal value of a parameter of the son wavelet function is obtained by minimization of the wavelet entropy. The accuracy of this new technique is confirmed by applying it to a numerical example, and to an acoustic enclosure. The advantage of using the wavelet transform method over the Fourier-based modal analysis that would normally be used for the enclosure modes problem is established.     

SOLUTION OF COUPLED ACOUSTIC PROBLEMS: A PARTIALLY OPENED CAVITY COUPLED WITH A MEMBRANE AND A SEMI-INFINITE EXTERIOR FIELD

There have been many attempts to understand the coupling phenomena between a solid structure and the surrounding fluid. However, the studies were restricted to interaction only between a structure and a finite cavity or a structure and acoustic field of infinite size. The system that we have studied has a structure that faces both a cavity of finite size and an external field of semi-infinite size. We also allow a hole, which can directly interact with the cavity as well as the external field. This configuration, therefore, provides two different interactions, or communication means. One is the finite structure and the other is the hole of finite size. This paper studies as to how these two components interact with the other two systems: the finite cavity covered by the structure and the hole, and the semi-infinite fluid. For simplicity, a two-dimensional and partially opened cavity coupled with a membrane and an exterior field was selected. The solution has to be found by solving a boundary value problem, but this case has to do with the boundaries that have two different conditions: one is the membrane and the other is the hole. The solution has been found in terms of the modal functions that satisfy the boundary conditions of finite cavity, membrane and hole. Non-dimensional coupling coefficients are obtained from the solution. The results exhibit that the coupling effect gives additional peaks and troughs in the averaged pressure of the cavity. These peaks and troughs are symmetrically arranged with respect to Helmholtz frequency of the cavity. The strong coupling occurs at the trough frequencies where the membrane interacts actively with the cavity and the exterior field.     

层内突进传质扩散数学模型及求解

针对窜流型油藏的特点,抽象出物理原型,同时考虑纵向和横向扩散,建立层内突进传质扩散数学模型.应用拉普拉斯变换,求得层内突进传质扩散数学模型的解析解,并得到小段塞情况下的解析解.应用通用有限元分析软件,建立层内突进传质扩散的几何模型,并求得层内突进传质扩散数学模型的数值解.绘制层内突进传质扩散数学模型的浓度分布二维剖面及不同时间步的浓度变化剖面;通过无因次距离和无因次浓度关系及孔隙体积与无因次浓度关系可以看出,贝克莱特(Pe)数越大,峰值浓度越高,见剂时间越晚.通过解析解及数值解结合的方法,可加深对传质扩散本质的理解.     

Optimal Filtering Applied to the Inversion of the Laplace Transform

Inversion of the Laplace transform, used in the laser scattering measurement of colloidal particle size distributions, presents severe numerical difficulties. In the presence of noise the variance of the inversion integral is infinite, indicating maximum uncertainty in the inversion. This paper applies the method of minimum variance, or “optimal”, filtering to the eigenfunction spectrum of the Laplace transform, giving an inversion which has finite variance. Spectral decomposition using the eigenfunctions of the Laplace transform gives a representation of the noise and desired signals analogous to the Fourier spectrum used in linear system theory. It is possible to obtain a filtered estimate of the unknown linewidth distribution. The requirement that the variance of this filtered estimate is minimum leads to a Wiener-Hopf integral equation defining the optimal filter. The results of this paper provide a basis of comparison of all methods of inversion of the Laplace transform, including the extensive literature of colloidal particle sizing by laser scattering or photon correlation.     

On the durable critic load in creep buckling of viscoelastic laminated plates and circular cylindrical shells

Based on the first order shear deformation theory and classic buckling theory, the paper investigates the creep buckling behavior of viscoelastic laminated plates and laminated circular cylindrical shells. The analysis and elaboration of both instantaneous elastic critic load and durable critic load are emphasized. The buckling load in phase domain is obtained from governing equations by applying Laplace transform, and the instantaneous elastic critic load and durable critic load are determined according to the extreme value theorem for inverse Laplace transform. It is shown that viscoelastic approach and quasi-elastic approach yield identical solutions for these two types of critic load respectively. A transverse disturbance model is developed to give the same mechanics significance of durable critic load as that of elastic critic load. Two types of critic loads of boron/epoxy composite laminated plates and circular cylindrical shells are discussed in detail individually, and the influencing factors to induce creep buckling are revealed by examining the viscoelasticity incorporated in transverse shear deformation and in-plane flexibility.     

Acoustic characteristics of annular cavities with locally non-uniform media

A theoretical approach is developed to obtain the natural frequencies and the mode shapes of annular cavities that have locally non-uniform media. The equation of motion is derived based on a special form of the wave equation that is capable of representing the variation of material properties with position, and the unit step function is used in the equation to express the local non-uniformity of the media. The Laplace transform is adopted in eigenvalue analysis to calculate the natural frequencies and the normal mode shapes of the annular cavities. The validity of the presented method is verified through finite element analysis and experiments. Parametric studies are performed to find out the relation between the acoustic characteristics of the cavity and the local deviation of the media, and the acoustic characteristics are explained in terms of the mass and stiffness effect of the local deviation in an annular cavity upon the natural vibration characteristics.     

Analytical prediction of break-out noise from a reactive rectangular plenum with four flexible walls

This paper describes an analytical calculation of break-out noise from a rectangular plenum with four flexible walls by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The breakout noise from rectangular plenums is important and the coupling between acoustic waves within the plenum and structural waves in the flexible plenum walls plays a critical role in prediction of the transverse transmission loss. The first step in breakout noise prediction is to calculate the inside plenum pressure field and the normal flexible plenum wall vibration by using an impedance-mobility approach, which results in a compact matrix formulation. In the impedance-mobility compact matrix (IMCM) approach, it is presumed that the coupled response can be described in terms of finite sets of the uncoupled acoustic subsystem and the structural subsystem. The flexible walls of the plenum are modeled as an unfolded plate to calculate natural frequencies and mode shapes of the uncoupled structural subsystem. The second step is to calculate the radiated sound power from the flexible walls using Kirchhoff-Helmholtz (KH) integral formulation. Analytical results are validated with finite element and boundary element (FEM-BEM) numerical models.     

Periodic shunted arrays for the control of noise radiation in an enclosure

This work presents numerical and experimental investigations of the application of a periodic array of resistive-inductive (RL) shunted piezoelectric patches for the attenuation of broadband noise radiated by a flexible plate in an enclosed cavity. A 4×4 lay-out of piezoelectric patches is bonded to the surface of a rectangular plate fully clamped to the top face of a rectangular cavity. Each piezo-patch is shunted through a single RL circuit, and all shunting circuits are tuned at the same frequency. The response of the resulting periodic structure is characterized by frequency bandgaps where vibrations and associated noise are strongly attenuated. The location and extent of induced bandgaps are predicted by the application of Bloch theorem on a unit cell of the periodic assembly, and they are controlled by proper selection of the shunting circuit impedance. A coupled piezo-structural-acoustic finite element model is developed to evaluate the noise reduction performance. Strong attenuation of multiple panel-controlled modes is observed over broad frequency bands. The proposed concept is tested on an aluminum plate mounted in a wooden box and driven by a shaker. Experimental results are presented in terms of pressure responses recorded using a grid of microphones placed inside the acoustic box.     

Vibro-acoustic behaviors of an elastically restrained double-panel structure with an acoustic cavity of arbitrary boundary impedance

An analytical study on the vibro-acoustic behaviors of a double-panel structure with an acoustic cavity is presented. Unlike the existing studies, a structural–acoustic coupling model of an elastically restrained double-panel structure with an acoustic cavity having arbitrary impedance on sidewalls around the cavity is developed in which the two dimensional (2D) and three dimensional (3D) modified Fourier series are used to represent the displacement of the panels and the sound pressure inside the cavity, respectively. The unknown expansions coefficients are treated as the generalized coordinates and the Rayleigh–Ritz method is employed to determine displacement and sound pressure solutions based on the energy expressions for the coupled structural–acoustic system. The effectiveness and accuracy of the present model is validated by numerical example and comparison with finite element method (FEM) and existing analytical method, with good agreement achieved. The influence of key parameters on the vibro-acoustic behaviors and sound transmission of the double-panel structure is investigated, including: cavity thickness, boundary conditions, sidewall impedance, and the acoustic medium in the cavity.