随机地震激励作用下自复位结构的平稳响应

自复位结构是一种震后不需修复或仅需少量修复即可继续投入使用的新型抗震结构。目前有关自复位结构地震响应的研究多是在确定性激励下进行,鲜有涉及随机激励环境。假定地震动加速度过程为金井清过滤白噪声模型,研究了随机地震激励下单自由度自复位体系的平稳响应。应用广义谐波平衡技术分解旗帜形的恢复力,建立原系统的等效非线性随机系统。通过Stratonovich-Khasminskii极限定理作随机平均,得到关于幅值的近似一维扩散过程。建立并求解对应的FPK方程,得到关于幅值的稳态概率密度函数并进行参数分析。数值结果表明,能量耗散系数与屈服位移的减小能降低系统响应,同时,随着这两个参数的变化,系统会出现随机P分岔现象。通过蒙特卡罗数值模拟法验证了解析解的有效性。

Stationary response of self-centering structure under random earthquake excitation

Self centering structure is a new type of aseismic structure which can be put into use without repair or with only a small amount of repair after earthquake.At present,most of studies on seismic response of self-centering structure are performed under deterministic excitation,and few involve random excitation environment.Here,the stationary response of a single-DOF self-centering system under random seismic excitation was studied,and the acceleration process of the ground motion was assumed to be Kanai-Tajimi filtered white noise model.The generalized harmonic balance technique was used to decompose restoring force of flag shape,and the equivalent nonlinear stochastic system to the original system was established.By means of Stratonovich-Khasminskii limit theorem and stochastic averaging,an approximate one-dimensional diffusion process for amplitude was obtained.The corresponding FPK equation was established and solved,the analytical solution to the steady-state probability density function for amplitude was obtained and this function’s parametric analysis was done.Numerical results showed that decrease in energy dissipation coefficient and yield displacement can reduce response of the system;with variation of these two parameters,the system can have random P-bifurcation phenomenon.Finally,the effectiveness of the analytical solution was verified with Monte Carlo numerical simulation method.