本文之主旨在於使用有限元素法來求數種曲形樑的自然頻率與振態，以及這些曲形樑承受移動負荷作用時的強迫振動反應。因為一曲形樑的面內與面外特性不同，故通常都被分開來研究，本文亦採用這種方式，各別推導一曲形樑元素的面內與面外運動的性質矩陣。其中，各二維樑元素的勁度矩陣是從力與位移的關係式求得，而質量矩陣則從動能方程式求得，為使本文理論，能同時適用於薄樑與厚樑，吾人在推導曲形樑元素的性質矩陣時，曾將剪切變形與旋轉慣性矩效應，全部納入考慮。接著，吾人將所有曲樑元素的性質矩陣加以組合，並施加指定的邊界條件，以求得整根曲樑的總勁度矩陣及質量矩陣。根據這些性質矩陣，吾人便可求得一曲樑的面內與面外振動的自然頻率與振態，若再考慮移動負荷所引起的外施負荷向量，吾人亦可求得該曲形樑承受移動負荷作用時的強迫振動反應。除了傳統的圓弧形曲樑外，由一片段曲樑的兩端，各連接一片段直樑所構成的混合式曲樑，其動態特性本文亦加以探討。上述吾人使用曲樑元素所得的結果，除了與現有文獻比較外，亦與使用傳統直樑元素所得的結果相比較，以各項結果良好的吻合，來證明本文理論與電算程式的可靠性。

The objective of this thesis is to determine the natural frequencies and mode shapes of the curved beams and the forced vibration responses of these beams subjected to moving loads by using the finite element method. Because the in-plane and out-of-plane characteristics of a curved beam are different, the associated dynamic behaviors of a curved beam are usually studied respectively. For this reason, the property matrices for the in-plane motions and those for the out-of-plane motions of a curved beam are also derived respectively in this paper. In which, each two-dimensional (2-D) stiffness matrix of a curved beam element is obtained from the relations between forces and displacements, while each 2-D element mass matrix is obtained from the equation of kinetic energy. To assure the presented theory to be available for both the thin curved beams and the thick curved beams, the effects of shear deformation and rotary inertia are taken into consideration when the above-mentioned property matrices of the curved beam element are derived. Next, the last element property matrices are assembled and the specified boundary conditions are imposed to establish the overall stiffness and mass matrices of the entire curved beam. Based on these overall property matrices, one may determine the natural frequencies and mode shapes of in-plane and out-of-plane vibrations of a curved beam and the associated forced vibration responses due to moving loads. In addition to the classical circular curved beam, the dynamic characteristics of a hybrid beam composed of a curved beam segment connecting two identical straight beam segments at its two ends are also studied. The numerical results obtained from the presented curved beam elements are compared with both the existing literature and those obtained from the conventional straight beam elements, the excellent agreement between the associated results assure the reliability of the presented theory and the computer programs developed for this paper.

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