Two dimensional finite-difference time-domain formulation for sound propagation in a temperature-dependent elastomer-fluid medium

This study focuses on the two-dimensional finite-difference time-domain (FDTD) formulations to investigate the acoustic wave propagation in elastomers contained in fluid region under different thermal conditions. The developed FDTD formulation is based on direct solution of the time-domain wave equation and the Havriliak-Negami (H-N)dynamic mechanical response of the elastomers. The H-N representation including double fractional derivative operators can be accurately transferred from the frequency-domain to the time-domain by using Riemann-Liouville theory and the Grunwald-Letnikov operator for fractional derivative approximations. Since the Williams-Landel-Ferry (WLF) shift function is related to the relaxation time for different thermal conditions, the proposed scheme represents a simple and accurate prediction of acoustic wave propagation for varying thermal conditions. The pulse-wave propagation in viscous fluid field is simulated by investigating the Navier-Stokes equations. The acoustic properties of different elastomers in a variety of temperatures are obtained by means of the proposed FDTD formulation and validated by a good agreement with the experimental data over a wide frequency range. Additionally, the 2-D examples relevant to wave propagation in different elastomers contained in a fluid field are implemented. The proposed FDTD formulation can be used to predict 2-D acoustic wave propagation in different thermal conditions accurately.