| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 93 === This article presents the random walk method which is developed for solving partial differential equations apply to problems of wave propagation and thickness shear mode.
The random walk method is based on the properties of diffusion processes, the Ito formula, the Feynman-Kac formula. To establish the relations between the unknown function, the boundary condition and the stochastic processes. Then we can use the principle of statistics find the probabilistic solution of the Laplace, Poisson, and Helmholtz equations.
We start by the scheme of the ray method, but instead of seeking a solution of wave equation in the Liouville product form. Then we can use the random walk method to find the approximate solution of the wave equation. Take the common wave propagation phenomenon as the example, discuss the feasibility of the random walk method applying to wave propagation. Finally will use the method in the end of this article, will discuss under each kind of frequency, the thickness vibration behavior problem.
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