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

This study focuses on the two-dimensional (2-D) finite-difference time-domain (FDTD) formulations to investigate the acoustic wave propagation in elastomers contained in a fluid region under different thermal conditions. The developed FDTD formulation is based on a 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 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 a 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.