【摘要】 能力谱方法是一种简化的结构抗震非线性分析方法,ATC-40等文件采用它来预测结构的力和位移需求。然而,ATC-40能力谱方法对一些非弹性系统的求解出现不收敛现象。现利用混沌动力学理论对ATC-40能力谱方法的收敛问题进行分析。ATC-40能力谱方法等效线性化迭代求解非弹性体系的位移,形成一个离散非线性映射或差分方程。对于这一离散动力系统,随着控制参数的变化,给出了动力系统迭代解的分岔图,展示了解的周期振荡、倍周期分岔、混沌等复杂动力学现象,阐明了能力谱方法迭代过程周期振荡解产生的原因。计算了动力系统的Lyapunov指数,从而判定系统解的运动状态和稳定性。最后指出了实现能力谱法等迭代算法收敛振荡控制的途径———混沌控制。更多还原

【Abstract】 The capacity spectrum method is a simplified nonlinear analysis procedure for seismic design of structures,the demands of forces and deformations of inelastic system can be predicated,and the methool has been incorporated into the ATC-40 document.However,the iterative procedure of the capacity spectrum method in the ATC-40 procedure A do not converge for some inelastic systems.The convergence analysis of the capacity spectrum method in ATC-40 is studied by using the theory of chaotic dynamics.The deformation of inelastic system is solved iteratively by using the equivalent linearization for ATC-40 capacity spectrum method,which forms a discrete nonlinear map or difference equation.For discrete dynamical system,the bifurcation plots of iterative solution of the system are presented with the change of controlling parameters.And the bifurcation plots show that there are the complicated dynamics phenomena for the solutions such as the periodic oscillation,period-doubling bifurcation,chaos and so on.The essential factors of periodic solution from iterative calculation of the capacity spectrum method are studied.The Lyapunov exponent of the dynamic system is computed,which is used to identify the motion state and stability of solutions.Finally,the chaos controlling on the convergent oscillation of iterative algorithms including capacity spectrum method is suggested.更多还原