Daiji Takahashi

Sound radiation from periodically connected double-plate structures

Abstract The problem of sound radiation from periodically connected infinite double-plate structures excited by a harmonic point force is investigated theoretically. Structures treated in this paper are the following three types: point connected, point connected with rib-stiffening, and rib-connected. Comparative consideration is given to the radiated sound power by a parametric survey. The results are applicable to problems of structureborne noise control in buildings.

Sound absorption of a cavity-backed membrane: A step towards design method for membrane-type absorbers

Abstract 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.

Sound transmission through a microperforated-panel structure with subdivided air cavities.

The absorption characteristics of a microperforated-panel (MPP) absorber have been widely investigated, and MPPs are recognized as a next-generation absorbing material due to their fiber-free nature and attractive appearance. Herein, further possibilities of MPPs are investigated theoretically from a sound transmission viewpoint. Employing an analytical model composed of a typical MPP and a back wall with an infinite extent, transmission loss through the structure is obtained. Although MPP structures generally have great potential for sound absorption, an improvement in the transmission loss at midfrequencies, which is important for architectural sound insulation, is not sufficient when using a backing cavity alone. Hence, to improve transmission loss at midfrequencies, an air-cavity-subdivision technique is applied to MPP structures. By subdividing the air cavity with partitions, each cell can create a local one-dimensional sound field as well as lead to a normal incidence into the apertures, which is the most effective condition for Helmholtz-type resonance absorption. Moreover, by providing the same motion as the back wall to the MPP, the sound-insulation performance can be further improved at midfrequencies.

Acoustic properties of permeable membranes

Membranes used for building materials have a certain degree of acoustic permeability, which has been disregarded in general membrane‐vibration theory, and may cause serious effects especially on the acoustic properties. In this study, a theory for sound absorption of, and sound transmission through, a single permeable membrane is developed. Subsequently, sound absorption of structures composed of air layers, absorptive layers, and the facings of permeable membranes is investigated theoretically, and discussed in comparison with the experimental data measured by using the reverberation‐room method. The results are in fairly good agreement; thus the present theory should give an effective tool for prediction of the acoustic properties of this type of membrane structure.

Detailed analysis of the acoustic properties of a permeable membrane

Abstract 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.

Wave propagation in ground-structure systems with line contact

The response of a structure in contact with the surface of a viscoelastic half-space (VEHS) is considered. The system is modeled as a ground-structure system. Vibration and radiation of sound into the closed space of the structure, resulting from a harmonic line force applied on the surface of the VEHS, are investigated theoretically. Stress-displacement relationships of the contact area are formulated by using modified forms of Lambs integral solutions for an elastic half-space as Green functions. A set of integral equations formulated by using this procedure is evaluated and numerically calculated. The structure is modeled as one of thin plates, and the response can be determined in the form of flexural and quasi-longitudinal waves. Also, acoustic coupling between the flexural modes of vibration and the air is presented as a spatially averaged sound pressure level based on the assumption of a perfectly diffuse sound field.

Reflection of a spherical sound wave by an infinite elastic plate driven to vibration by a point force

Abstract 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.

Effects of an air-layer-subdivision technique on the sound transmission through a single plate

Many studies on the sound transmission through a single plate have been carried out theoretically and experimentally. The transmission-loss characteristics, in general, follow mass law. Therefore, increasing mass of a plate is a fundamental measure to improve the insulation performance. This method, however, has limitations and might not be a reasonable alternative in current standards. Furthermore, the transmission loss at the critical frequency of coincidence is deteriorated significantly even if the mass is rather large. In this paper, the effect of the air-layer-subdivision technique is studied in detail from the viewpoint of the sound transmission problem of a single plate. An analytical model of an infinite single plate with a subdivided layer is considered and the improvement of the transmission loss is estimated. The limitations of the technique are clarified with some parametric studies. In order to validate the predictions, an experiment was carried out. The transmission loss of a glass board with the air layer subdivided by acryl partitions was measured in the experiment. They were in good agreement with the theoretical ones near and above the coincidence.

Wave propagation in ground-structure systems, Part I: Analysis of the model with surface contact

Abstract A simple two-dimensional model composed of a structure lying on a viscoelastic half-space (VEHS) with a continuous flexible interface is considered as a ground-structure system. Structural vibration and sound radiation into the closed space of the structure resulting from a harmonic line force applied on the ground surface are investigated theoretically. The structure is modeled as thin plates and the ground-structure interface is assumed to be perfectly bonded in both horizontal and vertical directions. Boundary conditions at the edges of the base plate cannot be expressed in an explicit form, such as free, simply supported or clamped, and so the fundamental modes of vibration also are unknown. Therefore, a modified Fourier series expansion method, which can be applied to problems with arbitrary boundary conditions, is used to obtain an approximate solution to the present problem. Relations between the Fourier component of the displacement and the corresponding stresses are formulated by using the Green function approach in the form of integral equations which can be solved numerically, regardless of the upper structure. Consequently the unknown coefficients of the components can be obtained as a result of the response of the whole system.

Effects of Air-Layer Subdivision: A New Method of Improving Sound Insulation:

In the impact of floors, sound transmission through walls, and structure-borne sound transmission in buildings, there is a possibility of improving the insulation by restricting the air particle motion at the interface of the vibrating surface and the air. One of the practical ways for realizing this condition is by subdividing the air layer at the interface in the direction parallel to the radiating surface. This novel method for noise control has an attractive simplicity and a real practical benefit. In this paper, the mechanism, causing this effect, is discussed using analytical models of acoustic radiation and sound transmission. As a result of this investigation, it is seen that the effect of this method is characterized by reduction of acoustic radiation at low frequencies near and below the critical frequency of coincidence. The method is validated experimentally.