Finite-difference time-domain analysis in porous materials by using Z-transform theory and infinite impulse response filter design

Abstract

Porous materials are wildly used to control noise in various places. When simulating sound field containing porous materials by Finite-difference time-domain (FDTD) method, it is necessary to develop FDTD formulations in the porous materials. When the frame of the porous material is motionless, the porous material can be replaced on the macroscopic scale by an equivalent fluid. Based on the equivalent fluid model, FDTD formulations in the porous material are developed. The method combines IIR (Infinite impulse response) filter design and Z transform theory. The effective bulk modulus and the effective density of the porous material are frequency dependant, which is designed as IIR filter. Wave equations with IIR filter modeled parameters are solved in Z domain to avoid troublesome convolution integrals in the time domain. At the Z domain, new parameters are assumed to simplify the wave equations. Finally, wave equations and assumed parameters are returned back to the time domain. The accuracy of the proposed method is verified with the measurement. As two application examples, porous material coved with permeable membrane or non-permeable membrane are simulated and compared with the theory.