本論文探討樑結構受到函數型時變性彈簧邊界拘束的振動問題。對於線性邊界問題，可使用移位函數法(Shifting function method)將邊界作移位，使系統簡化為較易處理的齊性邊界條件，再結合特徵函數展開法求解出系統之近似解。並探討彈簧係數為週期函數時，系統之暫態行為，以及受到外力強迫振動時的穩態行為，可發現其共振頻率將會受到時間與彈簧係數變化頻率的影響。

This study discusses the dynamic analysis of a beam with functional time-dependent linear spring coefficient. The shifting function method has been used to simplify and solve the 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 approximated solution with good convergence of the beam system can be reconstructed. One can investigate the influence of the boundary parameters on transient solutions and steady state solutions.

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