本文提出移動四自由度彈簧-阻尼-質量元素（由一個集結質量zvm 、二個滾輪質量zrim ( 1, 2 i  )、二個彈簧zik ( 1, 2 i  )與二個阻尼zic ( 1, 2 i  )所組成）的理論來進行承受移動負荷之長方形板的振動分析，以便將移動負荷的旋轉慣 性效應、平移慣性效應、彈簧效應與阻尼效應納入考慮。在本研究中，上述移動四自由度彈簧-阻尼-質量元素的元素特 性矩陣是由移動彈簧-阻尼-質量(SDM)系統的動態平衡方程式推導而得。由於彈簧-阻尼-質量系統與支撐長方形板間的交 互作用效應已利用形狀函數將其考慮在上述元素特性矩陣內部，因此，元素特性矩陣將隨其瞬時位置而變化，而整體振 動系統的特性矩陣也將隨著變化。最後，本文將利用Newmark 直接積分法來求解整個結構系統的運動方程式，並計算整 體結構系統的動態反應。一些與本研究相關的重要參數（例如：移動SDM 系統的速度、彈簧常數、集中質量的中心位 置）將加以探討，由本文所提出的數值結果可以發現，上述參數對移動SDM 系統與長方形板的影響相當大。

To take the pitching, inertia, spring and damping effects of moving load into account, the moving four-degree-of-freedom spring-damper-mass element, which consists of a lumped mass zvm , two roller masses zrim ( 1, 2 i  ), two springs zik ( 1, 2 i  ) and two dampers zic ( 1, 2 i  ), is presented in this paper. Based on the dynamic equilibrium equations of the four-degree-offreedom (dof) moving spring-damper-mass (SDM) system, the element property matrices of the presented element are derived. The interactions between the moving SDM system and the plate are considered, by means of shape functions, in the last matrices. Because the element property matrices of the presented element vary with its instantaneous position on the plate, they are timedependent matrices, so are the overall property matrices of the entire vibrating system. Dynamic responses of the structural system are calculated by solving the equations of motion of the entire vibrating system with Newmark integration method. Some factors, such as moving speed, spring constants and the position for centre of gravity of lumped mass of the SDM system, closely relating to the title problem are investigated. Numerical results show that the influences of the foregoing parameters on the dynamic responses of the moving subsystem and the plate are considerable.