Maxwell粘滞阻尼器耗能结构的随机地震响应

Structures Response in Random Earthquake for Maxwell Viscous Dampers

对Maxwell粘滞阻尼器耗能单自由度结构在Kanai-Tajimi谱地震激励下的随机响应进行了系统研究,建立了结构运动方程,将随机平均法运用于结构的微分与积分混合运动方程,结构的响应幅值近似为一维Markov扩散过程,获得了扩散过程漂移系数和扩散系数的解析表达式,利用扩散过程与FPK方程的对应关系,获得了幅值概率密度函数、幅值任意阶矩和结构响应能量任意阶矩的解析解;利用幅值和相位角与结构位移和速度的相互转化关系,获得了结构位移与速度联合概率密度函数和位移、速度方差以及位移期望穿越率的解析解。算例表明:当阻尼器的阻尼系数cb和广义支撑刚度kb增大时,结构随机响应减小,减震效果增强。

The random earthquake response of SODF structures with Maxwell dampers in Kanai-Tajimi spectrum earthquake is studied systematically.The dynamic equations of structure are established.The structural amplitude diffusion process and the analytical formulas of the drift and diffusion coefficients are got by stochastic averaging method.The exact solutions of probability density and arbitrary-order moments of amplitude and structural energy are got by mutual relationship between diffusion process and FPK equation.The exact solutions of joint probability density and the mean-square values of displacement and velocity,and the exact solution of the expected rate of displacement threshold crossings are achieved by mutual relationships between structural amplitude,phase,displacement and velocity.Tests show that the damping coefficient cb and the generalized support stiffness kb increase,while the random response of the structure reduces.The damping effect increases.