分数导数粘滞阻尼器减震结构的随机地震响应与等效阻尼

Random Earthquake Response and Equivalent Damping of Dissipation Structures with Fractional Derivative Viscous Dampers

对分数导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。建立了结构运动方程;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和位移、速度响应方差的解析解;基于与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,算例分析表明了所得公式的合理性。

Random earthquake response and equivalent damping of SDOF dissipation structure with fractional derivative viscous dampers are studied systematically. The dynamic equations of structure are firstly established. By the stochastic averaging method, structural amplitude is approximated to diffusion process, the exact solutions of joint probability density and mean-square values of structural displacement and velocity are completed. From equivalent criterion of stochastic averaging analysis, the analytics formulas of equivalent damping of fractional derivative viscous dampers are established. Thus it is possible for structure to use response spectrum. An example is shown in these methods, and the proposed formula is analyzed.