本文旨在於應用混合微分轉換有限差分法解決非線性彈性拘束邊界樑之強迫震動問題。混合微分轉換有限差分法的概念是結合有限差分法以及微分轉換法，可以用來於求解非線性偏微分方程，這個方法之概念是將偏微分方程中的兩個自變數拆成兩個系統，而後分別使用有限差分法與微分轉換法，並同時對兩者進行計算求解。藉由混合微分轉換有限差分法，可以解決單純使用微分轉換法無法處理系統，並同時保有高準確度。
文本開頭先介紹微分轉換法之原理、性質、基礎定義與各種應用。而後利用Bernoulli-Euler樑理論與Hamilton原理推導非線性邊界樑系統之統御方程式與時變之非線性邊界條件，並利用混合微分轉換有限差分法求解問題。
考慮一均勻樑兩端受到彈性拘束與非線性支撐，並受一橫向外力，求解此樑之暫態撓度。文中分別探討樑變形為大、小撓度時，旋轉彈簧係數、線性位移彈簧係數、非線性彈簧係數、外力參數與尺寸參數對撓度變化的影響，觀察並比較其之間的關係。
研究結果得知，撓度會隨著線性位移彈簧參數、非線性位移參數、旋轉彈簧參數、尺寸參數上升而下降。旋轉彈簧參數同時可以降低邊界撓度與中心撓度之差距，維持樑形狀穩定。振動速度會隨著線性位移彈簧參數、非線性位移參數增加而增加，隨著尺寸參數上升而下降。考慮變形為小撓度時，非線性位移彈簧之影響十分微小。在考慮變形為大撓度時，非線性位移彈簧對撓度之影響會隨外力變大而增加。

In this article, the hybrid differential transform and finite difference method is used to analyze the forced vibration of beams with non-linear elastically end restrained boundary conditions. The hybrid method which combines the differential transform method and finite difference method is employed to reduce the partial differential equations of the beam to a set of discrete algebraic equations. To obtain dynamic forced response of the beam, the governing equation is transformed to the algebraic equation by hybrid differential transform and finite difference method. Solve the deflection of the beam and investigate the effect transient response by dimensionless parameters including translational spring constant, non-linear translational spring constant, rotational spring constant, scale parameter and distributed loads parameter.

The results show that the transient deflection gets lower by the upper translational spring constant, the upper non-linear translational spring constant, the upper rotational spring constant, and the upper scale parameter. The difference between the deflection of boundary and the deflection of center of beam gets lower by the upper rotational spring constant. The speed of vibration gets faster by the upper translational spring constant, the upper non-linear translational spring constant, and lower scale parameter. In the large deflection, the effect caused by non-linear translational spring constant is more obvious than the small deflection.

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