Two-dimensional finite-difference time-domain formulation for sound propagation in a temperature-dependent...

Area of Science:

• Acoustics
• Materials Science
• Computational Physics

Background:

• Acoustic wave propagation in elastomers is crucial for various applications.
• Understanding the influence of thermal conditions on elastomer acoustics is complex.
• Existing models may not fully capture the dynamic mechanical response of elastomers.

Purpose of the Study:

• To develop and validate a two-dimensional finite-difference time-domain (2-D FDTD) formulation for acoustic wave propagation in elastomers.
• To investigate the impact of varying thermal conditions on elastomer acoustic properties.
• To accurately model the dynamic mechanical response of elastomers using the Havriliak-Negami (H-N) model.

Main Methods:

• Direct solution of the time-domain wave equation coupled with the Havriliak-Negami (H-N) dynamic mechanical response.
• Transferring the H-N representation to the time-domain using Riemann-Liouville theory and Grunwald-Letnikov operator for fractional derivative approximations.
• Simulating pulse-wave propagation in a viscous fluid using Navier-Stokes equations.

Main Results:

• The proposed 2-D FDTD formulation accurately predicts acoustic wave propagation in elastomers under different thermal conditions.
• The model successfully incorporates the Havriliak-Negami (H-N) dynamic mechanical response and its thermal dependence via the Williams-Landel-Ferry shift function.
• Simulations showed good agreement with experimental data over a wide frequency range.

Conclusions:

• The developed 2-D FDTD formulation provides a simple and accurate method for predicting acoustic wave propagation in elastomers at various temperatures.
• This approach is effective for modeling complex wave phenomena in elastomer-fluid systems.
• The study offers a valuable tool for analyzing elastomer behavior in diverse thermal environments.