黏彈性基礎儲油槽之水平與垂直地震反應及其相互之影響

Abstract

本研究主要探討液體於剛性儲存槽中受 到水平及垂直外力震動時之沖激(sloshing)行 為，以及與底部隔震結構之互制反應。本文 採用滿足勢流(potential flow)理論之流體，利 用二維與三維邊界元素法求解流場邊界上之 速度勢及速度梯度分布。再以Lagrangian 座 標描述法並配合泰勒級數展開式，計算分析 自由液面上質點運動現象。於求得水槽內液 體與自由液面之動力反應之後，進而利用白 努利方程式(Bernoulli’s equation)求取槽壁四 周壓力分布以及底部剪力。並將底部剪力施 加於所附加之結構物上，建立液體與結構互 制反應方程式，再採用狀態空間法(state space)於離散時間域求解各項結構動力反 應，以探討液體與結構互制效應與特性。本 文以液體儲存槽及其附加隔震裝置後之動力 反應進行數值模擬計算。同時，也進行一系 列小型結構實驗，針對上述應用例題以實驗 方式探討其動力特性，並與數值計算結果作 交互驗證。

The numerical approach for the liquid sloshing phenomenon inside a rigid tank subjected to a horizontal or vertical excitation is established first. The liquid is assumed to satisfy the assumptions of potential flow. Therefore, the Boundary Element Methods with the Lagrangian coordinate description and Taylor series expansion are applied to solve the non-linear sloshing problem. The hydrodynamic pressure on the tank wall is obtained by the Bernoulli’s Equation, and the base shear force due to liquid sloshing can be calculated by the integration of the hydrodynamic pressure along the tank wall. Then the base shear force is applied on the structure to simulate the interaction between liquid and structures. Then the space state vector method is treated to solve the transient structural responses. Hence, the interaction between liquid tanks and isolators can be studied by the present numerical scheme in detail. In this study, both numerical simulations and scaled model tests are adopted for the investigations of the seismic isolation of rigid liquid-storage tanks. The agreements between the numerical and experimental results are very good.