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对多自由度带支撑Maxwell粘滞阻尼器减震结构的随机响应特性进行了系统研究。建立了结构一般运动方程;将运动方程按原结构振型展开,将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;基于多自由度随机平均法理论,获得了结构随机平均It方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;根据SRSS组合方法,给出了耗能结构随机地震响应方差的一般解析式,从而建立了此类耗能结构随机响应特性分析的完备解析解法。
The random response characteristics of Maxwell viscous dampers with multiple degrees of freedom support structure are systematically studied. The general equation of motion of the structure is established. The equation of motion is expanded according to the original structural mode shape, and the equation of motion is transformed into the differential and integral mixed seismic response equations of modeled generalized coordinates. Based on the multi-degree-of-freedom stochastic mean method theory, It equations derived generalized analytic solutions of amplitude and phase transient joint probability density function, displacement and velocity transient joint probability density function, displacement and velocity transient response variance for each mode oscillator of energy dissipation structure. According to the analytic formula of SRSS combination method, a general analytical expression of the random seismic response variance of the energy dissipation structure is given, and a complete analytical solution to the random response characteristics of such energy dissipation structures is established.