In this paper we propose a model for sound-absorbing poroelastic materials using the homogenization method, based on the asymptotic approach. In contrast to the conventional Biot's model which is empirical and is not linked with the microstructure, the proposed model is consistent with microscopic structure and yields a macroscopic governing equation with properties predicted directly from microscopic geometry. In this model, four properties for the solid phase and two properties for the fluid phase are calculated by averaging characteristic functions of the periodic microscale model. These properties are then substituted into the macroscopic governing equations to evaluate performance such as the sound absorption coefficient for normal incidence. The proposed model is reduced to an equivalent monophasic model, i.e., an elastic solid model when the pore size is infinitely small, and a fluid model governed by the Helmholtz equation when the bulk modulus of the solid phase is sufficiently high compared to the bulk modulus of the fluid phase. Utilizing two-dimensional models with simple microscopic geometries where analytical solutions of sound absorption coefficients for normal incidence can be obtained, we show that the proposed method can provide accurate numerical solutions that converge to solutions obtained analytically as the discretization parameter of the microstructural model is made smaller. We also show how the actual size of the microscale affects the sound absorption coefficient, using a three-dimensional microstructure model.
|ジャーナル||Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C|
|出版ステータス||Published - 2010 8|
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