钢制储液罐的Lyapunov特征指数及弹性动力失稳

为全面评估钢制储液罐在地震激励下的动力稳定性能,由压力-位移格式的流固耦合模型建立等效动力扰动方程,采用时变几何刚度矩阵参数化结构域抗力,修正广义扰动变量并实时调整向量模长,进而步进求解动态Lyapunov特征指数,分别在简谐地面加速度与地震激励下对某10万m3油罐进行动力稳定分析.结果表明:上述Lyapunov方法确定的动力不稳定域与Floquet方法基本一致;Lyapunov方法与B-R准则法计算的临界地震动峰值存在10%左右的最大相对误差;抗风圈有助于抑制动力不稳定域并提高临界地震动峰值.上述Lyapunov方法适用于二阶动力系统,可考虑地震持时影响且不限制地震波特性,大幅降低了动力稳定分析的计算成本并能满足工程应用精度.

Lyapunov Characteristic Exponents and Dynamic Elastic Instability of Steel Liquid Storage Tanks

Abstract： To comprehensively evaluate the dynamic stability of liquid storage tanks under earthquake excitations, the equivalent dynamic perturbation equations were established based on coupled fluid solid model with displacement pressure form, the resistance force in structure domain was parameterized by time varying geometric stiffening matrix, the generalized perturbation variables were then modified and the vector length was adjusted in real-time, and the dynamic Lyapunov characteristic exponents were then solved with time-stepping techniques, by which the dynamic stability analysis of a 100 000 m3 oil storage tank was respectively executed under harmonic and earthquake ground motions. The results show that the dynamic instability regions obtained by the above Lyapunov method were essentially consistent with the estimates of Floquet method, and the maximum relative error of critical peak ground acceleration calculated by Lyapunov method and B-R criteria method is appoximately 10 %, and the wind girders are helpful to inhibit dynamic instability regions and improve the critical peak ground acceleration. The proposed Lyapunov method is suitable for second order dynamic systems, can consider the effect of earthquake duration, and does not restrict the characteristics of seismic waves. Moreover it also dramatically reduces the computing cost of dynamic stability analysis and meets the precision requirement for engineering application.