Yasuhito Kawai

The application of integral equation methods to the calculation of sound attenuation by barriers

Abstract Diffracted fields by thin rigid or absorbent barriers are investigated theoretically by using integral equations derived from Helmholtz-Kirchhoffs formula and from its normal derivative. The surface of the barrier is divided into elements to solve the integral equations numerically and the potential is assumed to be uniform on each element. For the numerical treatment of the integral equations in three dimensions, the integral including the strongly singular kernel is evaluated by the line integral along the edge of the element; this reduces the amount of computation and avoids the difficulty due to singularity. A numerical method which removes the problem of singularity is also presented to solve the integral equations in two dimensions. Some numerical examples are presented to demonstrate the effectiveness of this method. Moreover, for a flat rigid barrier, farfield solutions in the high frequency range are evaluated asymptotically on the basis of Kirchhoffs boundary conditions and compared with exact solutions.

A numerical method for the calculation of transient acoustic scattering from thin rigid plates

Abstract The scattering of a transient spherical wave from a thin rigid plate is investigated both theoretically and experimentally by using the integral equation derived from the normally differentiated Kirchhoff formula. The surface is divided into elements to solve the integral equation numerically and the contribution from each element is evaluated by the line-integral along the boundary of each element on the assumption that the potential is uniform in each element at each instant. This reduces the amount of computation and avoids the difficulty due to singularities. Some examples are presented to demonstrate the effectiveness of the method.

Calculation of Sound Fields Over Audience Seats by Using Integral Equation Method

The integral equation derived from normally derived Helmholtz-Kirchhoffs formula (NDF) is used to solve this problem. In numerical calculation, it is assumed that the seats are composed of rigid plates of negligible thickness and the potential is uniform in each divided surface element

Modeling and formulation of microperforated panels in the finite-difference time-domain method

A microperforated panel (MPP) was first developed by Maa and is recently regarded as one of the most promising absorption materials for next generation. Considering the approximation formula suggested by Maa, impedance of the perforations cannot be directly implemented in time-domain calculations because the impedance depends on frequency. Some new ideas are therefore necessary to take into account the effects of an MPP in time-domain analyses. Herein, a method to consider effects of an MPP in the finite-difference time-domain (FDTD) analyses is proposed. An MPP is considered as a boundary condition and the frequency dependence in the calculation is removed by replacing the frequency-dependent terms with constant values which are derived based on the multiple regression analysis. Additionally, the stability condition of the MPP boundary for one-dimensional sound field is developed. Absorption characteristics of MPP absorbers with back air layers of various depths are calculated numerically and compared wi...

Acoustic Property Simulation for Building Components

This chapter shows practical examples of numerical simulation results for acoustical characteristics of building elements, such as the sound absorption, sound-scattering, and sound insulation performance. Additionally, radiation characteristics of speaker systems are also treated. In each section, methodologies and numerical modeling schemes of the simulation, and the calculated results for practical cases are illustrated. The results are validated through comparison with the measurement results, and the applicability of the numerical methods is discussed.

Noise Propagation Simulation

This chapter shows examples of numerical analyses on various noise propagation problems including outdoor noise propagation, noise barriers, depressed roads, building facades, building windows, and floor impact sound. In each section, considering the features of each problem, methodology of applying the simulation techniques presented in Part I to the practical problem is introduced and the calculated results are illustrated. Some of the calculated results are compared with measured ones and the applicability and efficiency of the analysis method are discussed.

The application of boundary integral equation methods to the numerical calculation of transient waves in rooms

The boundary integral equations derived from Kirchhoff’s formula and its normal derivative form are available for the numerical calculation of transient waves in rooms. The two equations are compared in view of the stability and accuracy in the numerical calculation of responses in a rigid cubic room in which rigorous responses can be obtained by the image method. Some source waves and some problems appear in the numerical implementation such as the singular integrals, and the treatment of absorbent surfaces is also investigated. Finally, it is shown that the boundary integral equation method is a powerful tool to obtain transient waves in rooms.