| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 91 === In this study, we adopt the method of fundamental solutions (MFS) to simulate the two-dimensional stream function, the two-dimensional Stokes equations, the two-dimensional Helmholtz equation, and two-dimensional thin plate vibration problem. Our objective is to use the MFS to solve the Bi-Harmonic equations that are widely employed in the theory of thin plate and slow flow problems. Some reasonable assumptions have been made on the boundary conditions for the stream function. Comparison of the results by MFS to the results from FEM reveals that both are very close. On the other hand, we made some asymptotic assumptions of the fundamental solutions for thin plate vibration problem to simulate the two dimensional stream function and the numerical results show that our asymptotic behaviors have been justified.
In thin plate vibration problems, we will deal with the governing equation with the homogeneous boundary conditions. In order to find out meaningful non-trivial solutions, we utilize the singular value decomposition (SVD) method to detect the eigenvalues and eigenmodes. Therefore in order to justify the correct usage of the SVD method, we have simulated two dimensional Helmholtz equation with homogeneous boundary condition, and compared with the analytical solutions. The result indicates that the MFS is very accurate and efficient as far as computational aspects are concerned. Furthermore, we utilize singular value decomposition (SVD) method to solve the thin plate vibration problem and the eigenfrequencies have been obtained efficiently by employing the clamped boundary conditions for circular thin plates.
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