本篇論文研究主要著重於樑結構的具函數型時變性彈性係數的振動做問題探討。只要是線性邊界問題，都可使用變數變換法，將邊界作移位，系統之邊界即可簡化，經此簡化可使系統之運算較易處理。本文利用微擾法(Method of Perturbation) 將系統拆解轉換成多組線性時變型邊界受時變型函數所影響的系統，之後再利用變數變換法(Shifting Function)求解出各系統之近似解。而在其中結合變數變換法時可以使其中近似解中之微擾量解的形式可以找出一組具規律性的遞迴關係式(Recursive Formula)，其求解之過程會相當簡易。本論文提供之方法可應用於目前任意形式的函數型時變型齊性邊界的樑結構系統振動問題

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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