Infinite Rigid Baffle Research Articles

Comparison of Acoustic Radiation Characteristics in the Near and Far Fields Due to the Vibration of a Circular Disk Placed on an Infinite Rigid Baffle Using the Rayleigh Integral Method and Lumped Parameter Method

Comparison of Acoustic Radiation Characteristics in the Near and Far Fields Due to the Vibration of a Circular Disk Placed on an Infinite Rigid Baffle Using the Rayleigh Integral Method and Lumped Parameter Method

The imaginary part of the diffuse field forced normalized radiation impedance of a rectangular panel

This paper modifies previous approximate formulae for calculating the imaginary part of the azimuthally averaged forced normalized radiation impedance experienced on one side of a rectangular panel mounted in an infinite rigid plane baffle by a forced travelling wave on the rectangular panel which is excited by an infinite plane sound wave incident at an angle to the normal to the rectangular panel on one side of the rectangular panel. This modification is made so that the formulae can be analytically integrated over all possible solid angles of incidence on one side to obtain formulae for the imaginary part of the diffuse sound field forced normalized radiation impedance of the rectangular panel. The paper also gives existing formulae for the real part of this diffuse sound field forced normalized radiation impedance. The reason for developing approximate formulae for the imaginary part of this diffuse sound field forced normalized radiation impedance is so that they can be used when approximating the equation for the diffuse field sound transmission coefficient of a limp single leaf wall.

Acoustic radiation efficiencies of laminated composite structure under mechanical excitation and hygrothermal loading: Numerical analysis

In this research, the sound radiation efficiencies of multi-layer composite flat as well as curved structure under harmonic mechanical excitation in hygrothermal environment is numerically investigated using a coupled micromechanical finite element and boundary element scheme. The higher-order mid-plane kinematics including the stretching effect is equipped for the structural modeling and the Hamilton’s principle is utilized to evaluate the hygro-thermo-elastic natural frequencies alongside corresponding modes of the structures lying on an infinite rigid-baffle. An isoparametric Lagrangian element with zero order Hermitian interpolation function (ten degrees of freedom per node) is utilized for transforming the continuous structural equations into discrete counterparts. The effective composite material properties due to combined hygrothermal loading are considered via a micromechanical model. Then, an indirect boundary element method is employed to attain the structure-surrounding coupling and the sound radiation efficiencies are computed by solving the Helmholtz wave equation. The effectiveness of the model is established by converging it with the similar results available in the open literature for vibrational as well as sound radiation efficiencies and the results reveal the confirmation of the model accuracy. Upon solving diverse numerical illustrations, the sound radiation efficiency found to decrease with intensity of hygrothermal loads and the cross-ply spherical panels with less volume fraction of fiber depicted the least RE values over the entire frequency range considered.

Sound transmission through baffled multilayered curved shells using a transfer matrix method

The present work describes the use of a transfer matrix method to define the acoustic behavior of multilayered and periodic baffled curved shells consisting of a generic arrangement of homogeneous and heterogeneous periodic layers of various nature (fluid, solid, and poroelastic). The dynamic stiffness matrix of a unit cell is manipulated in order to derive the through-radius transfer matrix of a cylindrical periodic layer. Thus, the acoustic radiation or transmission of multilayered shells can be assessed. The blocked pressure field due to an incident plane wave is defined by taking into account the infinite rigid baffle by means of a two-dimensional boundary element model. Analytical expressions for the cylindrical acoustic impedances are utilized to define the coupling with the bounding fluid media. Furthermore, a one-dimensional windowing technique is adopted to account for the finite length of the shells. The proposed approach is validated by systematic comparison with a full finite-boundary element method.

Interface reflection wave of axisymmetric directional spherical-wave

The sound radiation field of a circular piston source in an infinite plane rigid baffle can be approximated as an axisymmetric directional spherical-wave. The interface response expressions of the axisymmetric directional spherical-wave for the piston parallel with the interface has already been obtained in previous studies. On condition that the distance from the piston center to the interface is much greater than the piston radius, we first derive the conical wave expansion of the axisymmetric directional spherical-wave which is obtained by using the conical wave expansion of the homogeneous spherical-wave and the formula of the axisymmetric directional spherical-wave excited by a circular piston in an rigid infinite plane, and then derive the expression of the interface reflection wave of the axisymmetric directional spherical-wave for the piston non-parallel to the interface. The expression of the interface reflection wave is simplified into a simplified expression by saddle point method on condition that the source distance is much larger than the acoustic wavelength. The simplified expression is not only simple in the calculation, but also clear in the physical meaning. The simplified expression shows that the interface reflection wave of the axisymmetric directional spherical-wave can be regarded as the product of the axisymmetric directional spherical-wave excited by the piston mirror image and the reflection coefficient. The calculations show that when the piston radius is smaller than the acoustic wavelength, the reflected wave is less sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is weak. When the piston radius is greater than the acoustic wavelength, the reflected wave is very sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is strong. Increasing the angle included between the piston and the interface, the reflected wave and its directivity both first increase and then decrease. The reflected wave is largest and the directivity of the reflected wave is strongest when the angle included between the piston and the interface is equal to that between the interface normal and the connecting line between the mirror image of the piston center and the receiving point.

Sound radiation from plates with elastic boundary conditions embedded in an infinite perforated rigid baffle

Sound radiation from plates with elastic boundary conditions embedded in an infinite perforated rigid baffle (PRB) is analyzed in this paper. Based on the wavenumber domain approach and the solution for transverse vibration of plates with general elastic boundary conditions, the sound power and the radiation efficiency of the plates embedded in the PRB (named ‘PRB-ed plate’ in the following) are derived theoretically. By comparing with the results of sound radiation from baffled and unbaffled plates, it can be found that the PRB-ed plates behave like the dipole source radiation in the fundamental mode region as the perforation in PRB introduces communication of the sound field, while not sufficient to reach the lowest radiation efficiency as unbaffled cases. The parametric analysis of boundary conditions shows that the PRB-ed fully free plate has the lowest radiation efficiency below the critical frequency. For the cases of plates with constraints, the greater the constraints are, the lower the radiation efficiency is in the fundamental mode region, and this order will become totally opposite in the short-circuiting region. Further, the effects of PRB parameters on sound radiation from PRB-ed plates are compared. With the decrease of the PRB thickness and the hole diameter, or the increase of the PRB perforation ratio, the sound power radiated from PRB-ed plates is decreased below the critical frequency. This research could possibly provide ideas on the design of noise control for plate-like structures.

SOUND TRANSMISSION ACROSS A FINITE SIMPLY SUPPORTED DOUBLE-LAMINATED COMPOSITE PLATE WITH ENCLOSED AIR CAVITY

ABSTRACTSound transmission across a finite orthotropic laminated double-composite plate with enclosed air cavity on an infinite acoustic rigid baffle is investigated analytically. Sound velocity potential method combined with simply supported boundary conditions is used instead of traditional methods, has good scalability and is important for studies of acoustic vibration of structures. The sound transmission loss is calculated from the ratio of incident to transmitted acoustic powers. Specifically, the focus is placed on the effects of several key system parameters on sound transmission including the plate dimensions, the laminate configurations, the boundary conditions, and the composite materials are systematically examined.

Analytical Modelling of Sound Transmission Through Finite Clamped Double-Wall Panels with Magnetic-Linked Stiffness

A theoretical modelling approach is proposed for the vibroacoustic problem of sound transmission across a rectangular double-wall panel clamp mounted on an infinite rigid baffle with magnetically connected stiffness. The magnetic stiffness is derived based on interaction energy between the two rectangular magnets attached to the clamped plates. The exact solution for the vibration of the clamped double plates is taken into account by the method of modal function, and the dynamic response of the structures is obtained by employing the weighted residual (Galerkin) method. This method enabled the coupling of the acoustic and the magnetic stiffness of the link to be done effectively. The accuracy of the theoretical predictions is checked against existing experimental data, with good agreement achieved. The model is then compared with the theoretical formulation in a duct based on a low-frequency range with and without magnetic stiffness. The sound transmission loss (STL) of the two models agrees perfectly in the first resonance, but the mass–air–mass resonance frequency for the current model tends to shift towards a higher value. Furthermore, the influence of magnetic stiffness on the elevation angle and azimuth angle of the STL is investigated. The present method is suitable for double-panel systems with connecting stiffness for practical plates and is applicable for both low- and high-frequency ranges.

Recovery of non-stationary free field based on pressure and acceleration measurements in a noisy environment

In a noisy environment, the interested sound field is interfused with the non-stationary incoming field from the back side of the measurement plane and the scattered field caused by the incoming wave falling on the surface of the target source. In order to remove the non-stationary incoming and scattered fields simultaneously, a recovery method of the non-stationary free field with the pressure and particle acceleration measurements is proposed. First, the mixed time-evolving pressure and particle acceleration are firstly measured on one measurement plane, where the particle acceleration is obtained by the finite difference approximation with the aid of an auxiliary measurement plane; Then, two physical relations are employed to deduce a forward complete recovery formulation of the target source in the noisy environment. One relation contains two impulse response functions relating the time-wavenumber pressure spectrum to particle acceleration and pressure spectra, respectively, and the other is the surface reflection coefficient of the target source relating the scattered field to the incoming field. Finally, the mixed pressure and particle acceleration are substituted into the recovery formulation, and the time-evolving pressure radiated by the target source in free-field is recovered. Thereby, the proposed method possesses a significant feature of real-time recovery of the non-stationary free field. A circular piston fixed on an infinite rigid baffle and two monopole sources are designed in a numerical simulation to test the performance of the proposed method. The simulation results attest that the proposed method not only can recover the time-evolving pressure radiated by the target source in free-field at any space points, but also recover the space distribution of the non-stationary sound field of the target source in free-field at different time instants effectively. An experiment with two speakers embedded in a planar steel plate and a speaker is further employed to verify the validity of the proposed method.

Analytical modelling of sound transmission loss across finite clamped triple-wall sandwich panels in the presence of external mean flow

• The triple-wall panels have superior sound performance to their double-wall counterparts due to an additional partition. • The finite dimensions and clamped boundary influence the sound transmission of triple-wall sandwich panels. • The external flow enhances sound transmission loss significantly in the low-frequency domain. This paper analytically addresses the sound transmission loss (STL) performance of finite triple-wall sandwich panels lined with poroelastic materials and clamp mounted on an infinite rigid baffle in the presence of an external mean flow. The wave propagation in poroelastic media is addressed using Biot's theory. The coupling methods between the poroelastic core and facing plates are associated with different boundary conditions and various panel configurations. The Galerkin method and the modal superposition theory are used to deal with the clamped boundary conditions and finite extensions as well as to transfer the integral function to a matrix equation. The analytical model is verified by comparing to previous results of infinite triple-wall sandwich panels and finite triple-wall panels without poroleastic materials. The numerical results show that the triple-wall panels have superior STL to their double-wall counterparts due to the existence of an additional partition. The finite dimensions of the triple-wall sandwich panels with clamped boundary strongly influence the STL at low frequencies, and this effect is coupled with that of the external mean flow. The air layer plays a critical role in the sound insulation properties that vary among different panel configurations, and the configurations with two air layers exhibit the optimal overall sound insulation performance.

Sound radiation from a finite perforated panel set in a rigid baffle: A fully coupled analysis

A fully coupled formulation is presented for sound radiation from a finite flexible perforated panel set in an infinite rigid unperforated baffle. The panel is excited by a point harmonic force and radiates sound into the acoustic medium on both sides of the baffle. Prior to coupling with the fluid, the change in the inertial and stiffness properties of the panel due to perforations and their effect on the in vacuo natural frequencies and mode shapes are accounted for using the receptance method. The coupled acoustic and structural equations are formulated using the 2-D wavenumber transforms. Since the formulation is in terms of the panel velocity, a certain square root singularity that typically appears in the denominator is avoided. The self- and inter-modal coupling coefficients are evaluated either analytically or numerically. The radiated power, panel mean quadratic velocity and radiation efficiency plots are obtained for different perforation ratios for both center and off-center excitations. At first, our formulation is validated against an unperforated case using a study available in the literature. Next, for our perforated panel case, we assume that both the half-spaces are filled with the acoustic fluid. It is observed that the radiation efficiency decreases with the increase in the perforation ratio, irrespective of the surrounding acoustic medium. However, for the water-loaded panel, the radiation efficiency is found to be lower than when the panel is immersed in air. It is found that for a light fluid like air, a one-way coupled formulation is adequate. The natural frequencies of a water-loaded perforated panel are also presented. It is found that for a given mode, the natural frequency increases with increase in the perforation ratio.

Vibro-acoustic analysis of laminated composite plate structure using structure-dependent radiation modes-An experimental validation

In this article, the acoustic radiation responses of the layered composite flat panel in an infinite rigid baffle under the influence of harmonic point load and various support conditions are investigated numerically. The laminated composite flat panel responses have been computed using the ANSYS parametric design language code. The natural frequencies obtained using the current simulation model are matched with the earlier published values as well as in-house experimental results. The eigenvectors corresponding to the validated eigenvalues are extracted and utilised for the computation of the acoustic properties numerically by solving through Rayleigh integral scheme. The first radiation mode’s amplitudes for the vibrating plate have been computed and validated with the results available in open literature. Further, the self-radiation efficiency and radiated sound power are obtained based on the structure dependent radiation modes and all the radiation modes are also included to evaluate the exact radiated sound power. Finally, the effect of the different composite (Carbon/Epoxy and Glass/Epoxy) properties, constraint conditions and the location of point load on the displacement and velocity responses, radiation efficiency and the radiated acoustic power level of the layered flat panel have been investigated and discussed in detail.

Acoustic radiation and frequency response of higher-order shear deformable multilayered composite doubly curved shell panel – An experimental validation

In this article, the acoustic radiation responses of doubly curved laminated composite shell panels subjected to harmonic excitation are investigated numerically in the framework of the higher-order shear deformation theory. A general mathematical model for the vibrating curved panel has been developed and the cylindrical, spherical, elliptical and hyperboloid shell panel geometries resting on an infinite rigid baffle are considered for analysis. The desired response is computed using an in-house code developed in MATLAB. Firstly, the natural frequencies of the vibrating shell panel are obtained using the present model and validated with data available in the literature with experimental test results. A coupled finite element/boundary element formulation is then used to obtain the acoustic response of the structure. The mean square velocity, radiation efficiency and the sound power radiated are chosen as the acoustic response indicators. The effect of different support conditions, lamination schemes, aspect ratio and geometry of the vibrating doubly curved shell panel on the acoustic radiation behaviour is investigated and discussed in detail. It is observed that the support conditions and the lamination scheme greatly influence the acoustic radiation from the panels. On the other hand, the radiation pattern is quite similar for different geometries with a substantial distinction for flat plate.

Sound transmission through a finite perforated panel set in a rigid baffle: A fully coupled analysis

Sound transmission through a fluid-loaded finite perforated panel set in an infinite unperforated rigid baffle is considered. Using a fully coupled formulation in the 2-D wavenumber domain, the transmitted pressure due to an incident plane wave is obtained. The change in the panel resonances caused by the perforations is accounted for. The formulation also takes into account the self- and inter-modal coupling coefficients arising due to the fluid-loading effect. The derivation is almost entirely analytical with numerical computations done at the very end. Transmission loss (TL) curves are plotted for various cases and the physics is discussed. Along the way an uncoupled calculation is also done for the sake of comparison. The results are mainly for a light medium like air. For a light medium, in general, the perforate impedance is lower than the panel impedance. Thus, most of the transmission happens through the perforations. The panel velocity contribution is insignificant and hence the uncoupled calculation is adequate. In general, the absolute perforate impedance increases with increasing frequency. So does the TL. At low frequencies, because the resistive component of the hole impedance increases, the absolute perforate impedance rises. Thus, the TL curves rise at the lower frequencies. This effect is prominent for sub-millimeter hole radii, i.e., for micro-perforations. An important issue with the TL values for perforated panels is that they sometimes acquire negative values at low frequencies. This apparent anomaly is resolved by showing that at low frequencies there is an additional power component that flows from the baffle region onto the panel. Upon inclusion of this additional term, the TL values remain positive at all frequencies.

Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach

In this article, the vibration-induced acoustic responses of laminated composite flat panels subjected to harmonic mechanical excitation under uniform temperature load are investigated numerically. The natural frequencies alongside corresponding modes of the flat panels resting on an infinite rigid baffle are obtained by using finite element method in the framework of the higher-order shear deformation theory. A coupled finite and boundary element formulation is then employed to acquire the acoustic responses. The governing equation for the sound radiaiton from the vibrating structures is derived by solving the Helmholtz wave equation. The vibration and acoustic responses are computed by using the present scheme via an in-house computer code developed in MATLAB environment. In order to avoid any excess thermal loading conditions first, the critical buckling temperature of the panel structure is obtained and authenticated with the benchmark values. Further, the sound power levels for isotropic and laminated composite panels are computed using the present scheme and validated with the existing results in the published literature. Finally, the influence of lamination scheme, support conditions and modular ratio on the acoustic radiation behavior of laminated composite flat panels in an elevated thermal environment is studied through various numerical examples. The thermal load is found to have substantial influence on the stiffness of the panels and the peaks in the free vibration responses tend to shift to lower frequencies for higher temperatures. It is also inferred that the panels radiate less efficiently whereas the overall sound pressure level is found to follow an increasing trend with increasing temperature.

Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory

The vibro-acoustic responses of the laminated composite flat panel in an infinite rigid baffle under the influence of central and eccentric harmonic point excitation are investigated numerically. A general mathematical model of the flat panel is developed in the framework of the higher order shear deformation theory to compute the vibrational properties. The system governing equations are obtained using Hamilton’s principle and discretised through suitable finite element steps. An in-house computer code is developed based on a coupled finite and boundary element formulation in MATLAB environment and employed to compute the associated acoustic radiations from the vibrating plates. Lab scale experiments (modal analysis) are performed to validate the natural frequencies obtained using the present scheme. The proposed formulation is validated for acoustic responses by comparing the present sound power level with the results available in published literature alongside the results obtained using commercial finite element package (ANSYS). The validation study demonstrated the inevitability of the present formulation in predicting the vibro-acoustic response of the layered composite plate. The geometrical parameters (aspect ratio, thickness ratio), composite material properties, lamination scheme and support conditions are found to have significant influence on the vibro-acoustic behaviour of laminated composite flat panel.

Analytical modelling of sound transmission through finite clamped double-wall sandwich panels lined with poroelastic materials

This paper addresses analytically the vibroacoustic problem of sound transmission across a rectangular double-wall sandwich panel clamp mounted on an infinite rigid baffle and lined with poroelastic materials. The wave propagation in poroelastic media is described by Biot’s theory and the coupling methods between the poroelastic core and the panel determine the various configurations and associated boundary conditions. The modal superposition theory and the weighted residual (Galerkin) method are employed to account for the finite extension with the clamped boundary and to obtain a double-series solution of the problem through a matrix equation. The sound transmission loss (STL) of the structure is calculated for a single incident wave after validating the analytical model against previous theories and experiments. The numerical results show that the finite panel and clamped boundary influence the STL dominantly in the low-frequency range. The poroelastic materials exhibit strong damping effects on the resonances of STL spectra at high frequencies as well as panel vibrations and enhance significantly the sound insulation performance of the sandwich panel.

Expansions for the radiation impedance of a rectangular piston in an infinite baffle.

Relatively compact analytical expressions in the form of fast-convergin g expansions are derived for the radiation resistance and reactance of a rectangular rigid piston in an infinite rigid baffle, which are computationally efficient at high frequencies or large aspect ratios and yield simple approximations (asymptotic expressions) at low frequencies. Plots of the normalized radiation resistance and reactance are shown for various aspect ratios with constant width as well as constant area. Comparisons are also made with the impedance of an elliptic piston.

The acoustic radiation impedance of a rectangular panel

This paper extends the definition of the one sided radiation impedance of a panel mounted in an infinite rigid baffle which was previously used by the authors so that it can be applied to all transverse velocity wave types on the panel rather than just to the possibly forced travelling plane transverse velocity waves considered previously by the authors. For the case of travelling plane waves on a rectangular panel with anechoic edge conditions, and for the case of standing waves on a rectangular panel with simply supported edge conditions, the equations resulting from one of the standard reductions from quadruple to double integrals are given. These double integral equations can be reduced to single integral equations, but the versions of these equations given in the literature did not always converge when used with adaptive integral routines and were sometimes slower than the double integral versions. This is because the terms in the integrands in the existing equations have singularities. Although these singularities cancel, they caused problems for the adaptive integral routines. This paper rewrites these equations in a form which removes the singularities and enables the integrals in these equations to be evaluated with adaptive integral routines. Approximate equations for the azimuthally averaged one sided radiation impedance of a rectangular panel mounted in an infinite baffle are given for all the cases considered in this paper and the values produced by these equations are compared with numerical calculations.

The Effect of Plate Discretization on Accuracy of the Sound Radiation Efficiency Measurements

Abstract This paper deals with the problem of the effect of discretization level and certain other parameters characterizing the measurement setup on accuracy of the process of determination of the sound radiation efficiency by means of the Discrete Calculation Method (DCM) described by Hashimoto (2001). The idea behind DCM consists in virtual division of an examined sound radiating structure into rectangular elements each of which is further assumed to contribute to the total radiation effect in the same way as a rigid circular piston having the surface area equal to this of the corresponding virtual element and vibrating in an infinite rigid baffle. The advantage of the method over conventional sound radiation efficiency measurement techniques consists in the fact that instead of acoustic pressure values, source (plate) vibration velocity amplitude values are measured in a selected number of regularly distributed points. In many cases, this allows to determine the sound radiation efficiency with sufficient accuracy, especially for the low frequency regime. The key part of the paper is an analysis of the effect of discretization level (i.e. the choice of the number of points at which vibration amplitude measurements are to be taken with the use of accelerometers) on results obtained with the use of the method and their accuracy. The problem of determining an optimum level of discretization for given excitation frequency range is a very important issue as the labor intensity (time-consuming aspect) of the method is one of its main flaws. As far as the technical aspect of the method is concerned, two different geometrical configurations of the measurement setup were tested.