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对多自由度带支撑Maxwell阻尼器减震结构的等效阻尼比进行了系统研究。构建了耗能结构一般微分和积分混合地震响应方程组;基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析计算式。与一些典型问题的模态应变能法的计算精度进行对比分析,结果显示:本文方法的计算结果在特定条件下与精确解完全相同;在一个二自由度系统中相对位移响应方差的误差分别为0.99%和0.45%,优于应变能法的8%和5.4%,表明了本文方法的有效性。从而为建立此类耗能结构等效阻尼分析的完备解析解法、直接应用反应谱法进行实际工程设计提供了依据。
The equivalent damping ratio of Maxwell dampers with multiple degrees of freedom support structure is systematically studied. The generalized differential and integral mixed seismic response equations of dissipative structures are constructed. Based on the same equivalent criteria as the multi-degree-of-freedom stochastic average method, a general analytic formula for the equivalent damping ratios of various energy-dissipative structures is established. The results show that the calculation results of this method are exactly the same as the exact solution under certain conditions. The errors of the relative displacement response variance in a two-degree-of-freedom system are 0.99% and 0.45%, better than the strain energy method of 8% and 5.4%, indicating the effectiveness of this method. In order to establish the complete analytic solution of equivalent damping analysis of such energy-dissipating structure, the direct application of response spectrum method to provide the basis for actual engineering design.