Effect of membranes at microscopic polygonal faces of polyurethane foam by using homogenization method

Abstract

Sound absorption coefficient in poroelastic media depends on the geometries in the microscopic scale. In some polyurethane foams that exhibit high sound absorption coefficients in the middle frequency range around 1 kHz, the faces of polygonal shape of microscopic structure are covered by thin membranes. Moreover, a hole is frequently found in some membranes. This type of microscopic structure is considered to contribute to the high sound absorption performance. Multi-scale analysis for sound-absorbing poroelastic media with periodic microscopic geometries has been recently proposed by one of the authors. In this method, the homogenization method based on the asymptotic expansions are utilized and further extended to express the viscous dissipation in the vicinity of the boundary between the solid and fluid phases, thermal dissipation from the fluid phase to the solid phase. Analysis in the microscopic scale is first performed by using a unit cell of the periodic structure and macroscopic properties are derived. The properties are then applied to calculate macroscopic response such as sound absorption coefficient. In this paper, we apply this multi-scale analysis and investigate numerically the relationship between the size of the hole in membranes and sound absorption performance.