| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 97 === This study discusses the dynamic analysis of beam with functional time-dependent linear spring coefficient. We can use the shifting function to solve the linear boundary problem. The associated mathematic system is a fourth order ordinary differential equation with time dependent boundary conditions. It is shifted and decomposed into five linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. We use method of perturbation to decompose the system into many parts of beam problem with linear time-dependent boundary condition, and using shifting function to solve the separated system, finally, the beam system can be reconstructed. During the solving process, we can fine a regular recurrence formula between the separated systems which can reduce the solving process. For any form of the functional time-dependent boundary system, one can obtain approximate analysis solutions with good precision, and can investigate the influence of the boundary parameters on system by the present method
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