經振動台試驗結果證實正確設計之多項式摩擦單擺支承 (Polynomial Friction Pendulum Isolator，PFPI)，不論於遠域或近域地震皆可有效降低結構系統之位移。然而，將振動台試驗所得之垂直加速度加入一維動力分析後，發現支承垂直震盪間接影響水平力的變化與支承狀態改變的時間，使PFPI支承遲滯迴圈邊緣有不平滑的現象，可見垂直震盪會影響PFPI隔震支承的反應。 本研究將介紹PFPI之二維動力分析程式的內容，數值模擬的動態歷時反應採用Newmark-β法分析，並利用振動台試驗結果驗證分析方法之正確性。最後藉由一受震之PFPI隔震橋梁探討垂直震盪對PFPI隔震性能與考慮垂直向自由度對模擬PFPI隔震橋梁受震反應的重要性，並利用FPS與PFPI之二維動力分析程式，針對含FPS與含PFPI之隔震橋梁於雙向震波中分別進行最佳化設計，除比較兩者之隔震效益外，同時探討垂直震波對PFPI之影響、PFPI曲面之支承參數與PFPI曲盤形狀之修正方法。 ;Experimental results have proven that properly designed Polynomial Friction Pendulum Isolator (PFPI) can effectively reduce the isolator drift not only in a far-fault earthquake but in a near-fault earthquake. However, the vertical vibration affects the history of horizontal force and the variation time of bearing state when the vertical acceleration has been considered in one dimensional motion equations program for PFPI, it cause the edge of the hysteresis loop of PFPI not smoothly. So the vertical vibration has effect upon the response of PFPI. Consequently, two dimensional motion equations for PFPI isolated bridge were derived and presented in this paper. The responses of PFPI isolated bridge were solved by using Newmark-βmethod. The feasibility and correctness of solution procedures were verified by comparing the simulated responses with that measured from shaking table tests. A five-span PFPI isolated bridge subjects to ground excitations was then analyzed to demonstrate the effects of vertical vibration on the performance of PFPI and the importance of vertical free dimension. The optimal parameters study of PFPI and Friction Pendulum System (FPS) comparison the effectiveness between PFPI and FPS. Finally, the effects of considering vertical ground excitation, the function of PFPI sliding surface and the modification method for PFPI sliding surface were discussed in this study.