剛體晃動行為之研究

Abstract

本文探討剛性質塊之自由晃動及受水平地表擾動下之晃動行為。質塊在搖晃運動過程中，由於底座兩端的旋轉支點不斷地交替互換而消耗能量。惟當剛性質塊隨其高寬比增加時，伴隨晃動所產生之消能機制將逐漸喪失，亦即愈細長之結構其動能損失愈小。由解析解與數值解之比較，驗證朗吉-卡特法之正確合理，再進一步分析地震擾動時剛性質塊之晃動行為。分析結果顯示，當剛性質塊為細長結構(H/B>3)且晃動之初始角度不大時，其運動方程式可以線性化近似之。

In this thesis, the rocking behaviors of rigid blocks under both free-rocking and horizontal ground excitations are investigated. During the process of rocking, energy is dissipated by switching back and forth the rotation centers at the two toes of the block alternatively. However, as the height-to-width ratio of the rigid block increases, the energy dissipation due to rocking decreases. The numerical solutions by the fourth-order Runge-Kutta method has proved to be sufficient as compared with the analytical results. It is in turn used to analyze the rocking behavior of rigid blocks under earthquake excitations. Simulation results also indicate that, as the block is slender (H/B>3) and initial angle of rotation is small, the governing equation of rocking can be linearized with sufficient accuracy.