地震反应分析中Caughey阻尼系数的优化解

传统方法建立Caughey阻尼矩阵时,存在选择多个合理参考频率及避免负模态阻尼比的问题.为此,基于地震反应谱分析,以结构的峰值位移误差最小为优化目标,将模态阻尼比大于零为约束条件,提出了优化Caughey阻尼系数的约束二次规划方法.然后,以一个直径90米,高15米的穹顶结构为例,说明当不同动力反应的显著贡献模态不同,且相应的固有频率有巨大差异时,有必要采用Caughey阻尼矩阵.同时,分析比较了传统方法和优化方法对结构地震反应误差的影响.计算结果表明:传统方法选择的参考频率忽略了不同模态对动力反应贡献的差别,这导致不同激励下的动力反应的计算精度有很大差别;优化方法可使显著贡献模态的阻尼比合理,对于4阶以上Caughey级数,优化方法的计算误差都小于传统方法.

OPTIMAL SOLUTION OF CAUGHEY DAMPING COEFFICIENTS IN SEISMIC RESPONSE ANALYSIS

When the Caughey damping matrix is constructed by traditional method, how to choose reasonable multi-reference frequencies and avoid negative modal damping ratios are challenges. Therefore, based on the seismic response spectral analysis, using the error of peak displacement as the objective function and making the modal damping ratios larger than zero as constraint condition, an optimal solution of Caughey damping coefficients is proposed by constraint quadratic programming. Then, a dome structure with 90m-diameter and 15m-height is analyzed to illustrate the necessity of Caughey damping when there are many significant contribution modes and the difference in natural frequencies of significant contribution modes for different response are great. Meanwhile, the traditional method and the optimal method are compared in the effects on structural seismic response errors. Numerical results show that the traditional method ignores the difference in different modal contributions to choose reference frequencies and cannot control the errors of dynamic responses effectively; the optimal method makes the damping ratios of significant contribution modes reasonable and the errors from the optimal method is smaller than that of the traditional method for more than 4 Caughey series.