時間領域差分法による非フーリエ熱伝導方程式と連成された動熱弾性二次元平面き裂問題の数値解析

抄録

In recent years, a variety of microscopes using heat sources, such as photoacoustic microscopes, have been developed. In this observation principle, reflection and diffraction phenomena of two waves with different properties, namely thermal wave and elastic wave, are utilized. However, the thermal wave cannot be reproduced using the classical Fourier-type heat conduction equation. In order to overcome this mathematical difficulty, we had derived a coupled nonlinear partial differential equation consisting of the heat conduction with a delay time and the dynamic thermoelastic equation, and had simulated numerically the propagation process of thermal and elastic waves for one-dimensional problem. In this study, thermal and elastic waves were simulated for a two-dimensional plane problem with and without defect using the finite-difference time-domain method. The results showed that the reflection and interference phenomena of two waves can employ for detecting small internal defects existing near the surface of target sample.