带支撑分数导数粘滞阻尼器减震结构随机响应

Random response of the dissipation structures with the supporting brace and the in-line viscous dampers based on the fractional derivative model

对带支撑分数粘滞阻尼器单自由度耗能结构的随机地震响应与等效阻尼进行了系统研究。首先,建立结构运动方程;然后应用随机平均法,将结构响应幅值近似为扩散过程,获得了结构位移与速度联合概率密度函数以及位移、速度响应方差的解析解;最后,基于随机平均分析完全相同的等效准则,建立了可直接应用反应谱法的上述阻尼器的等效阻尼计算公式,给出了算例,并分析了所得公式的合理性。

The random earthquake response and equivalent damping of SDOF dissipation structure with the supporting brace and the in-line viscous dampers based on the fractional derivative model were studied systematically.The dynamic equations of the structure were established.Then,employing the stochastic averaging method,the structural amplitude diffusion was obtained,and the exact solutions of joint probability density function and mean-square values of structural displacement and velocity were given.Finally,using the equivalent criterion of stochastic averaging analysis,the analytic formulas of equivalent damping of the viscous dampers based on the fractional derivative model with supporting brace were established,which makes it possible to use the response spectrum in structures.An example using these methods was given.