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Permeable membranes (PMs), which are air-permeable thin woven fabrics or non-woven fabrics, are attractive sound-absorbing materials used to control acoustics in buildings. Although the absorption characteristics of various PM absorbers have been studied extensively, it has not been established how to incorporate PMs into a wave-based acoustic simulation method known as the time-domain finite element method (TD-FEM). This paper presents a numerical model of limp PMs for TD-FEM as well as a computationally efficient TD-FEM for predicting sound fields including PMs. The limp PM model incorporates effects of both sound-induced vibration of PMs and the air permeability of PMs. Consequently, two material parameters are considered: the surface density and flow resistance of PMs. Verification of the limp PM model and efficiency evaluation of TD-FEM were first performed with an impedance tube problem. Then, reverberation absorption coefficients of single-leaf PM absorbers with a non-locally reacting rigid backed air cavity were predicted through simulation of a reverberation absorption coefficient measurement using the present TD-FEM at frequencies of 100 Hz to 2.5 kHz. The predicted results were compared with measured and theoretical values. To demonstrate the applicability of present TD-FEM, eight PMs, each with different flow resistance and surface density, were considered for comparison. Results revealed that the present TD-FEM with the limp PM model can predict the magnitude relation of absorption characteristics of single-leaf PM absorbers attributable to differences of material properties of PMs.

Plane-wave-enriched finite element method (FEM), an efficient wave-based prediction method, uses shape functions incorporating a set of plane waves propagating in various directions to enhance the sound field approximation capability. The method can be an efficient wave-based acoustic solver for room acoustic simulations because it can simulate wave phenomena in rooms accurately with markedly fewer finite elements in spatial discretization than those used for standard FEM. However, several aspects remain to be addressed before its use for practical room acoustic simulations. Accurate sound absorber modelings able to address their frequency and incident angle dependence of absorption characteristics present extremely important issues. This paper presents a proposal of a method of implementing an extended-reaction model of microperforated panel (MPP) and permeable membrane (PM) sound absorbers into a room acoustic solver with plane-wave-enriched FEM. First, we demonstrate the validity of the proposed method in comparison with theoretical values in which impedance tube problems including three sound absorbers composed of MPP and PM are used. Then, the effectiveness over standard FEM is demonstrated via 2D real-scale office problems with the three MPP-PM sound absorbers.

Microperforated panel (MPP) absorbers, which provide broadband sound absorption without the use of fibrous materials, have favorable material properties that support recyclability, flexibility of design, hygiene demands, and cleaning. Many earlier studies have specifically examined the development of absorbers themselves. However, to use the absorption performance of MPP absorbers sufficiently in room acoustic applications, it is beneficial to develop accurate prediction methods of sound fields in rooms with MPP absorbers. Such methods are expected to be useful for room acoustics design and absorber design tools. This study constructs a frequency domain finite element (FE) solver for acoustic simulations of a practical sized room with MPP absorbers. Then the accuracy and effectiveness are evaluated. In the FE solver, spatial domains are discretized by fourth-order accurate FEs in terms of dispersion error, and MPP absorbers are modeled using first-order hexahedral limp MPP elements that can deal with sound propagation in the backing structure of absorbers. First, the accuracy of present FE solver is demonstrated using impedance tube problems in comparison with conventional second-order accurate FEs. Results show higher convergence of solutions for the present FE solver. Then, exploration of an iterative solver for efficient multi-frequency analyses reveals that the recently developed CSQMOR is a faster and more stable solver. Finally, comparison with a conventional surface impedance model based on a locally reacting assumption confirms the effectiveness of present FE solver by presenting the importance of dealing with the incident angle dependence of reactance of a rigid-backed air cavity in the modeling of single-leaf MPP absorbers.

Recent wave-based room acoustic simulations in the time domain can incorporate frequency-dependent absorbing boundary conditions (BCs), by which time responses including a broad frequency component are calculable with a single computational run. However, their performance over the frequency-domain method remains poorly understood. This paper presents a discussion of the capabilities of a recently developed implicit time-domain finite element method (TD-FEM) for room acoustics simulation by comparison with a fourth-order accurate frequency-domain FEM (FD-FEM). First, the implicit TD-FEM accuracy is examined via an impedance tube problem, having frequency-dependent absorbing BCs at the tube end, where a specific acoustic admittance ratio of rigidly backed porous sound absorbers is imposed. Results indicate that the implicit TD-FEM has the same solution convergence rate as that of FD-FEM. The solution converges to the FD-FEM solution when using a sufficiently small time interval. A performance comparison of both methods is then made using two real-scale 2D room acoustic problems in an office room and a complexly shaped concert hall. Numerical results show that the implicit TD-FEM can be useful for acoustic simulation in practical-sized rooms at broad frequency ranges with markedly smaller computational costs than those of FD-FEM while maintaining similar accuracy.

Because microperforated panels (MPPs), which can be made from various materials, provide wide-band sound absorption, they are recognized as one of the next-generation absorption materials. Although MPPs are typically placed in front of rigid walls, MPP space sound absorbers without a backing structure, including three-dimensional cylindrical MPP space absorbers (CMSAs) and rectangular MPP space absorbers (RMSAs), are proposed to extend their design flexibility and easy-to-use properties. On the other hand, improving the absorption performance by filling the back cavity of typical MPP absorbers with porous materials has been shown theoretically, and three-dimensional MPP space absorbers should display similar improvements. Herein the effects of porous materials inserted into the cavities of CMSAs and RMSAs are experimentally investigated and a numerical prediction method using the two-dimensional boundary element method is proposed. Consequently, CMSAs and RMSAs with improved absorption performances are illustrated based on the experimental results, and the applicability of the proposed prediction method as a design tool is confirmed by comparing the experimental and numerical results.

This paper presents the applicability of an explicit time-domain finite element method (TD-FEM) using a dispersion reduction technique called modified integration rules (MIR) on room acoustics simulations with a frequency-independent finite impedance boundary. First, a dispersion error analysis and a stability analysis are performed to derive the dispersion relation and the stability condition of the present explicit TD-FEM for three-dimensional room acoustics simulations with an infinite impedance boundary. Secondly, the accuracy and efficiency of the explicit TD-FEM are presented by comparing with implicit TD-FEM using MIR through room acoustics simulations in a rectangular room with infinite impedance boundaries. Thirdly, the stability condition of the explicit TD-FEM is investigated numerically in the case with finite impedance boundaries. Finally, the performance of the explicit TD-FEM in room acoustics simulations with finite impedance boundaries is demonstrated in a comparison with the implicit TD-FEM. Although the stability of the present explicit TD-FEM is dependent on the impedance values given at boundaries, the explicit TD-FEM is computationally more efficient than the implicit method from the perspective of computational time for acoustics simulations of a room with larger impedance values at boundaries.

As described herein, the sound insulation performance of a double window with absorbent materials on the perimeter of its cavity is studied experimentally. Two experiments are used to measure the sound reduction indices. The first experiment was performed with a double window composed of commercially available products. The second was conducted with a model constructed of two acrylic panels: a simplified model of a double window with a cavity between the panes. As the result of the first experiment, the improvement in reduction index obtained by the attached absorbent was around 4 dB. In the second experiment, though some negative effect was observed at low frequencies, the increase in reduction index was about 12 dB at maximum. Consequently, the following findings were obtained: (1) Acoustic transmission characteristics of a double window are affected mainly by resonances of two types: mass-air-mass resonance of window panes and the air cavity, and the acoustic mode resonances of the air cavity in-between; (2) acoustic mode resonance is suppressed by attaching absorbent materials on the inside of the cavity of window. Consequently, the sound reduction index increases.

A simple frequency-domain finite-element method (FD–FEM) for sound field analyses inside rooms installed with microperforated panel (MPP) sound absorbing structures is described here. This method can also analyze sound absorbing structures composed of MPPs and permeable membranes (PM) simply by changing the only material parameters of MPP into those of PM. As the first stage of the study, the validity of the present FD–FEM is tested through the numerical experiments based on the impedance tube method for measuring the absorption characteristics at normal incidence. In the numerical experiments, we calculated the absorption characteristics of a single MPP absorber, a double-leaf MPP space absorber and a space absorber composed of MPP and PM by using the FD–FEM in two-dimensions, and the computed absorption characteristics are compared with those calculated by an electro-acoustical equivalent circuit theory or a wave theory based on Helmholtz–Kirchhoff boundary integral equation. The results showed that the presented FD–FEM can analyze the absorption characteristics at normal incidence of the MPP sound absorbing structures accurately with the simplicity of the formulation.

Because microperforated panels (MPPs) can provide wide-band sound absorption without fibrous and porous materials, they are recognized as next-generation absorption materials. The fundamental absorbing mechanism is Helmholtz-resonance absorption due to the perforations and air-back cavity. Consequently, MPPs are usually placed in front of rigid-back walls. However, one of the authors has proposed MPP space sound absorbers without backing structures. Among these space absorbers, cylindrical MPP space absorbers and rectangular MPP space absorbers are advantageous due to their design flexibility and easy-to-use properties. Although their performances have been investigated experimentally, it is necessary to predict their absorption characteristics to develop improved shapes and efficient designs. Herein their absorption characteristics are numerically predicted using the two-dimensional boundary element method, and the applicability of a numerical method as a design tool to sufficiently predict the performance of MPP space absorbers is discussed.

A double-leaf microperforated panel absorber (DLMPP) is composed of a two microperforated panel (MPP) with a air cavity in-between, and without any backing structure. It shows a Helmholtz-type resonance peak absorption and additional low frequency absorption, therefore it can be used as a wideband space sound absorber. In this study, a theoretical study is made to examine the effect of a permeable membrane inside the air-cavity. Permeable membranes are studied in our previous studies and proved to be effective to improve the sound absorption performance of various type MPP sound absorbers. We investigate the absorption characteristics of a DLMPP with a permeable membrane in the cavity through numerical examples, and also studied the effect of honeycomb in the cavity of the same sound absorption structure.

This paper examines the sound insulation of a single-leaf wall driven by a spherical wave. The transmitted sound field of an infinite elastic plate under a spherical wave incidence is theoretically analyzed and insulation mechanisms are considered. The displacement of the plate is formulated using the Hankel transform in wavenumber space and the transmitted sound pressure in the far-field is obtained by Rayleigh’s formula in an explicit closed form. Moreover, a reduction index is also derived in a closed form by introducing an approximation into the vibration characteristics of the plate. Deterioration of the insulation performance under the spherical wave incidence is caused by an apparent decrease of wall impedance that depends on the directivity of the transmitted sound wave. The mass law for a spherical wave incidence is different from that for a normal plane wave incidence: doubling the weight of the wall or the frequency gives an increase of 3 dB (c.f. 6 dB for a normal plane wave incidence), which is also smaller than the field incidence mass law.

Panel-type sound absorbers are commonly used to absorb low-frequency sounds. Recently, a new type of panel/membrane absorbers has been proposed as a next-generation sound absorber free from environmental problems. On the other hand, it is known that placing a honeycomb structure behind a porous layer can improve sound absorption performance and a similar effect can be obtained for microperforated-panel absorbers. Herein, the sound absorption characteristics of a panel sound absorber with a honeycomb in its back cavity are theoretically analyzed. The numerical results are used to discuss the variations in the sound absorption characteristics due to the honeycomb as well as the mechanism for sound absorption.

The location of a vibration source within a machine is sometimes found to have a significant effect upon its radiated acoustic power. It is known that a simple reduction of vibration cannot always reduce the radiated acoustic power, so that treatments based on analysis of a structure’s vibration modes are not always effective. At the same time, radiation mode analysis is known to be a powerful tool for interpreting sound radiation since those modes are independent of a structure’s surface vibration. However, knowledge of the radiation modes alone cannot be used directly to understand the relationship between vibration source location and acoustic power radiation. In this paper, it is shown that the radiation mode concept can be extended to understand the relationship between acoustic power and driving force distribution by considering the product of the structure’s mobility matrix and the radiation modes: the resulting functions are here defined to be force radiation modes (frad-modes). An example is presented in which the acoustic power radiated by a simply-supported, baffled beam is reduced by using guidance provided by the structure’s force radiation modes. The results demonstrate that the force radiation modes can be used to guide the reduction of radiated acoustic power by changing the driving force location without the need to perform additional calculations or experiments.

So far the electro-acoustical equivalent circuit analysis has been widely used to analyse micro-perforated panel (MPP) absorbers, however, as for the double-leaf MPP the equivalent circuit analysis inevitably includes an approximation. In this paper, the sound absorption characteristics of a double-leaf MPP absorber backed by a rigid wall are analysed by wave theory using Helmholtz–Kirchhoff integral formulation to obtain a strict solution. The present wave theory is experimentally validated with existing measured results. The theory is also compared with the equivalent circuit solutions so that the differences between the two theories appear and the effect of the approximation is clarified. The comparison shows that the difference mainly appears in the vicinity of the resonance peaks: the differences occur in the resonance frequencies and the absorption coefficient at frequencies between the two resonance peaks.

With the aim to propose a reasonable and effective countermeasure for the elevated structure noise, the sound field radiated by a steel plate girder, which is the main source of the elevated structure noise, have been theoretically analysed. In the present study, steel plate girders are modelled as infinitely long elastic plate strips placed in parallel and numerical examples on the sound field radiated by the steel plate girders are shown. In the analysis of the radiated sound field, the equivalent source method is employed. Effect of the surface absorption on the sound field radiated by the girders is discussed through numerical examples. The results show that the surface absorption is effective for reduction of the radiated sound field, especially in the area that increase of sound pressure due to reflection by adjacent plate girders is observed. Furthermore, to design for reasonable countermeasure, variation of the noise reduction effect due to changing the pattern of surface absorption area on plate girders is classified.

A double-leaf microperforated panel space absorber (DLMPP) is composed of two microperforated panels (MPPs) placed in parallel with an air-cavity in-between, without a back wall or any backing structure. This was proposed as a space sound absorber, which can be used for a sound absorbing screen or partition. A conventional MPP absorber with a rigid back wall is effective only around its resonance frequency, which is usually at middle frequencies, and not effective at low frequencies. However, a DLMPP can be effective also at low frequencies, because an additional sound absorption is produced by its acoustic flow resistance. In the authors’ previous work, theoretical analyses on the acoustic properties of a DLMPP were carried out using a simplified electro-acoustical equivalent circuit model. However, the equivalent circuit model includes an approximation, and more sophisticated theory is required for a better prediction and detailed discussion. In this paper, a revised theory for a DLMPP is presented: A Helmholtz integral formulation is employed to obtain a rigorous solution for more precise prediction of the absorptivity of a DLMPP. The result of the present revised theory is compared with that of the equivalent circuit model, and the difference between them is discussed. A parametric survey is made through numerical examples by the present revised theory to discuss its acoustic properties.

The sound absorption mechanism of microperforated panel (MPP) absorbers and panel/membrane-type absorbers is both based on a certain resonance system and utilising its resonance effect. However, the relationship between the absorption mechanisms of MPPs and panel/membrane-type absorbers has not been discussed: it is not clarified whether they can occur simultaneously, or how they interfere each other. On the other hand, in a previous study there is an attempt to cause both absorption mechanisms simultaneously. In this paper, using an electro-acoustical equivalent circuit model, their sound absorption mechanisms and their relationship are discussed. In this study, three cases are considered: (1) the case in which only the mass reactance of the MPP is considered, (2) the case in which the losses of the panel is considered, and (3) the case in which the sound absorption of the back wall surface is considered. The results suggest that the microperforated panel absorption, which is Helmhotz-type resonance, and the panel/membrane-type absorption can be regarded as phenomena of the same kind which can be smoothly transformed into each other by changing a parameter, and can be consistently modelled and comprehensively discussed.

Microperforated panel (MPP) absorbers are promising as a basis for the next-generation of sound absorbing materials. MPPs are typically made of a thin metal or plastic panel. However, thin limp panels are generally not suitable as an interior finish of room walls because they do not have sufficient strength, which prevents practical application of MPPs as an interior finish of room walls. In order to overcome the lack of appropriate strength required for room walls, it is possible to make an MPP out of a thick panel. However, thick MPPs are usually not efficient because the resistance and/or reactance become too high. In this study, trial production of thick MPPs and measurement of their normal absorption coefficients were carried out. Results show that efficient absorption can be given with a thick MPP by using a tapered perforation.

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.

Microperforated panel (MPP) absorbers are promising as a basis for the next-generation of sound absorbing materials. Typically, they are backed by an air-cavity in front of a rigid wall such as a ceiling or another interior surface of a room. Indeed, to be effective, MPP absorbers require the Helmholtz-type resonance formed with the backing cavity. Towards the creation of an efficient sound-absorbing structure with MPPs alone, the acoustical properties of a structure composed of two parallel MPPs with an air-cavity between them and no rigid backing is studied numerically. In this double-leaf MPP (DLMPP) structure, the rear leaf (i.e., the MPP remote from the incident sound) plays the role of the backing wall in the conventional setting and causes resonance-type absorption. Moreover, since a DLMPP can work efficiently as an absorber for sound incidence from both sides, it can be used efficiently as a space absorber, e.g., as a suspended absorber or as a sound absorbing panel. The sound absorption characteristics of the double-leaf MPP are analysed theoretically for a normally incident plane wave. The effects of various control parameters are discussed through a numerical parametric study. The absorption mechanisms and a possible design principle are discussed also. It is predicted that: (1) that a resonance absorption, similar to that in conventional type MPP absorbers, appears at medium-to-high frequencies and (2) that considerable “additional” absorption can be obtained at low frequencies. This low-frequency absorption is similar to that of a double-leaf permeable membrane and can be an advantage compared with the conventional type of MPP arrangement.

This paper presents a method to predict the reverberation absorption coefficient of a finite-size membrane absorbers composed of a single- or double-leaf membrane structure of various configurations. In order to predict the sound absorptivity of such an absorber, it is needed to consider that sound is incident from both sides of the absorber, which has not been accounted for the previous studies on membrane absorbers. The edge effect also needs to be considered if the absorber is rather small. The present method is established based on the theory for absorbers hanged in a reverberation chamber developed by Fujiwara and Makita [J Acoust Soc Jpn (E) 1980;1:37–45]. The same theory requires the fraction of energy dissipation in the absorber, which can be obtained by the difference of absorption and transmission coefficients, and the difference is calculated by the theories for various membrane structures presented in the authors’ previous work. An experimental study was also conducted to validate the present method: the predicted values showed good agreement with the measured ones. The numerical examples calculated by the present method are also presented to discuss the effect of the various control parameters, and it is suggested how to improve the sound absorption performance of double-leaf membrane absorbers with a permeable and an impermeable leaves.

Double-leaf membranes with a permeable leaf on the sound incidence side are usually used as roofs in actual membrane-structure buildings. They are modelled as of infinite extent, and their acoustic properties are theoretically analysed. The theory is experimentally validated. The permeability can significantly improve the sound absorption performance at high frequencies, and makes the characteristics similar to those of cavity-backed porous absorbents. At low frequencies the permeability also affects the sound absorption and insulation performance. At middle frequencies, the characteristics changed according to the permeability: a mass–spring peak appears if it is very high, and vanishes if lower. These effects are strongly dependent upon the mass of leaves, flow resistivity, cavity depth, etc. A detailed discussion is also given to shed some light on the mechanism of these effects.

The sound radiation from a double-leaf elastic plate subjected to a point force excitation is investigated theoretically, to gain a fundamental insight into the sound radiation from an interior panel of a double-leaf structure in buildings. The effects of the interior panel on the sound radiation, which show a negative effect at low frequencies due to the mass–air–mass resonance, are discussed in detail. The theory is validated experimentally. As a measure of the efficiency of the interior leaf in reducing noise radiation, the radiation reduction is defined in this study, and it is found useful for predicting the sound radiation due to the structure-borne sound in building elements. Parametric studies through theoretical results are made to clarify the effects of the parameters of the sound radiation system, and to gain a fundamental insight into the control of structure-borne noise radiation. It is shown that it is difficult to reduce the radiated sound power by an interior panel alone, even if its mass is increased.

This paper describes the results of two subjective experiments to clarify the role of reflections arriving from behind the listener in the perception of spatial impression. The experiments investigate the effects of reflections from behind the listener on both listener envelopment (LEV) and auditory source width (ASW) and which is more effective for LEV, the early or late reflections. The results of experiments clearly show that: (1) The listener can perceive LEV and ASW as two distinct senses of a sound image. (2) The role of reflections arriving from behind the listener is to increase LEV in spatial impression. Namely LEV increases as the relative reflection energy of sound arriving from behind the listener increases. (3) The early reflections also contributes to the perception of LEV, while (4) the late reflections are more effective for LEV than the early ones. However, it cannot be definitely concluded whether C 80 affects LEV or not.

For understanding the phenomenon nature of the elevated structure noise around motorways, theoretical studies concerning the main source are needed. Steel plate girders of elevated motorways are the main source of the elevated structure noise. Considering the real conditions, it is necessary to clarify the effect of a concrete slab on the radiated sound field from a steel plate girder. In the present study, a steel plate girder in contact with a concrete slab is modelled by an infinitely long elastic plate strip in contact with a vertical reflecting surface. The method of equivalent sources is used. The sound field radiated by the elastic plate strip is illustrated by numerical examples. The main effects of a slab on the sound field are discussed. Furthermore, the variation of the effects due to the varying height of a plate girder is demonstrated. It is shown that a concrete slab does not affect significantly the sound field radiated by a plate girder in the range of 500–1000 Hz at most receiving points, which is the frequency range of the main interest in the study on the elevated structure noise.

The noise which is caused by vibration of steel plate girders of a motorway is studied. This type of noise is often referred to as elevated structure noise, and has its main component within the frequency range 500 Hz–1 kHz. Since a steel plate girder can be considered as a rectangular plate with an extreme aspect ratio, the sound field radiated by a baffled elastic plate strip of infinite length, which is the simplest model of a steel plate girder, was theoretically analysed in the preceding paper (Sakagami, K., Michishita, K., Morimoto, M., and Kitamura, Y. Sound radiation from a baffled elastic plate strip of infinite length with various concentrated exitation forces. Appl Acoust 55: 181–202). However, a real motorway construction is more appropriately modelled by an unbaffled strip. Thus the unbaffled condition has been analysed numerically in this paper. The method of equivalent sources is used. The main features of the radiated sound field are discussed in the light of numerical examples, and compared with those of a baffled strip. Two vibration patterns, i.e. an idealised piston vibration and flexural vibration excited by a moment are considered. Furthermore, in order to determine the far-field range of an infinitely long plate, the variation of the radiated sound field with the distance is discussed.

This paper analyzes the effect of an excitation force from a string instrument on the acoustic properties of a stage floor. The theory [9] Nakanishi S, Sakagami K, Daido M, Morimoto M. Effect of an air–back cavity on the reflected sound field of a spherical sound wave by an infinite elastic plate driven to vibration by a point force. Applied Acoustics, in press., for a spherical wave reflected by an air–cavity backed elastic plate driven into vibration by a point force, is modified. A measurement of an excitation force, exerted from a violoncello into a wooden riser, is performed. The numerical examples with the measured force demonstrate that the effect under consideration is significant at some frequencies. The modified theory explains the phenomenon called resonant support which is caused by the sound wave reflected by a rigid floor and the sound wave radiated from the riser top.

The effect of an air-back cavity on the spherical wave reflected by the stage floor is analyzed theoretically. An air-cavity backed infinite elastic plate is driven to vibration by a point force. A closed form expression for the far-field solution is derived by coupling the Helmholtz integrals for sound field and the equation of the plate motion. Numerical examples demonstrate four main features of the sound field. Two of them are absent for the plate without the air-cavity: one is a panel absorption dip owing to the plate and air-cavity resonance system. The other is small peaks and dips due to the acoustic resonances of the air-cavity.

This paper theoretically analyses the reflected sound field by an infinite elastic plate which generates its own sound field due to a point force excitation. The plate is a theoretical model for the stage floor. A closed form expression for the far-field solution was derived by coupling the Helmholtz equation for sound fields surrounding the plate and the equation of motion for the plate. The solution indicates that the field above the plate excited by a point force consists of the reflected sound by the plate at rest without the point force and the radiated sound from the plate excited by the point force. The general features of the field reflected by the vibrating plate with the point force excitation are discussed with the theoretical solution and numerical examples. The numerical examples are also presented to demonstrate the effects of the plate parameters on the sound field.

Recently, problems with elevated structure noise arise around elevated motorways, i.e. noise in the audio-frequency range supposed to be caused by the vibration of the structural elements of an elevated motorway. The measurement data shows that steel plate girders may be the main source of the elevated structure noise. Therefore, the radiated sound field generated by a baffled elastic plate strip of infinite length, which is the simplest model of the web of a steel plate girder, is theoretically analysed in this paper. A far-field approximation solution is derived in a closed form. Since the actual condition of the strip excitation has never been clarified so far, three kinds of possible concentrated forces, a line force, a point force, and a concentrated moment, are included in the analysis. The main features of the radiated sound field by the strip are discussed in the light of numerical examples. A parametric study is carried out to clarify the effects of the various parameters of the strip. Furthermore, solutions to the sound radiation from an elastic plate strip of finite length, under the same excitation conditions, are derived and compared with those from the strip of infinite length above. The characteristics of the finite strip are found to be roughly described by those of the infinite strip.

Low absorptivity is a problem associated with many membrane-structure buildings and can result in a long reverberation time which degrades the acoustic environment. One possible solution to this problem may be the use of membranes to form the ceiling. The present study examines the acoustic properties of double-leaf membranes, which have recently become widely used in the construction of membrane-structure buildings. Parametric studies with theoretically calculated results show the effects of various parameters on absorptivity and transmissibility. Experimental results confirm the theory. The possibility of using double-leaf membranes to construct the absorption structures is then discussed.

A detailed analysis is carried out to clarify the mechanisms governing the acoustic performance of a permeable membrane and the effects of various material parameters. For this purpose, the theoretical solutions for the reflected and transmitted sound fields by an infinite permeable membrane which have been derived in a previous paper [1] are approximated to obtain simple expressions for normal incidence absorption and transmission coefficients. An electrical circuit analogy is employed for a detailed analysis in which the particle velocity is separated into two components, i.e. the mass and the permeability, which is helpful in understanding their contributions to the acoustic properties of the permeable membrane. These considerations are aimed at demonstrating the effects of the parameters on the acoustic properties as well as explaining the following particular phenomena which are observed in the acoustic properties of a permeable membrane: the decrease of the sound energy absorbed in the structure at low frequencies and the increase of transmission loss at low frequencies due to the permeability. The optimal value of flow resistance for the most effective absorption is also obtained from those solutions.

This paper deals with a theoretical study of the sound absorption characteristics of a membrane-type sound absorber. A closed-form analytical solution for the sound absorption coefficient of an infinite membrane with an air-back cavity is produced by making a minor modification to the solution for a cavitybacked infinite elastic plate which was derived in the previous paper. To analyse the mechanism of absorption, the solution is rearranged in a form which points out the contribution of each element of a membrane-type sound absorber. The contribution of the cavity is found to be dominant, and that of the absorptivity of the source side surface of the membrane is rather small. In the case of an elastic plate, the contribution of the loss factor is found negligible. The effects of the parameters of the sound absorption system are discussed in the light of calculated results. Furthermore, the method to predict the peak-frequency and the peak value of the oblique-incident absorption coefficient of the membrane-type sound absorber is presented. The method satisfactorily explains the relationship between the absorption characteristics and the parameters. It is also applicable to panel absorbers. It can be useful for the design of the purpose-made membrane-type or panel absorbers, and for the sound field prediction within boundaries made from this type of absorber.