Rayleigh阻尼系数解法比较及对结构地震反应影响  

COMPARISON OF DETERMINATION METHODS FOR RAYLEIGH DAMPING COEFFICIENTS AND EFFECTS ON SEISMIC RESPONSES OF STRUCTURES

作　　者：潘旦光[1] 高莉莉[1] 

机构地区：[1]北京科技大学土木工程系,北京100083

出　　处：《工程力学》2015年第6期192-199,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51078032);北京市自然科学基金项目(8143037)

摘　　要：Rayleigh阻尼是一种广泛采用的正交阻尼模型。针对一个直径90m,高15m的穹顶结构,分析比较了四种方法(传统方法、最小二乘法、基于多参考振型的加权最小二乘法和基于结构位移峰值误差优化法)所得Rayleigh阻尼系数对结构地震反应计算精度的影响。四条地震波的分析结果表明:基于结构位移峰值误差的优化方法对于结构位移等以低阶模态控制的动力反应量计算精度最高;传统方法存在选择合适第二阶参考频率的难题;而最小二乘法不是计算Rayleigh阻尼系数的合理方法。当结构的显著贡献模态多且不同动力反应相关显著贡献模态的频率有巨大差异时,Rayleigh阻尼模型将无法构造兼顾低阶模态和高阶模态计算精度的阻尼矩阵,此时需要采用更多阶模态的阻尼比等于精确值的阻尼矩阵构造方法。Rayleigh damping is a common orthogonal damping model. The effects of Rayleigh damping coefficients on structural seismic response accuracies are discussed for a dome structure with 90m-diameter 15m-height. The following four methods are compared: a traditional method(TM), a least squares method(LS), a weighted least squares method based on multi-reference modes(WLS) and an optimization method based on minimizing the error of structure peak displacements(OM). The numerical results under four seismic excitations indicate that the OM is significantly more accurate than the other methods when significant contribution modes of responses are the first several natural frequencies, such as displacements. In the TM, one should take great care to select the reasonable second reference frequency. It is unreasonable to calculate the Rayleigh damping coefficients for the LS. When there are many significant contribution modes and the difference in natural frequencies of significant contribution modes for different response are great, it is impossible for Rayleigh damping to construct a damping matrix which makes the dynamic responses of the lower and higher modes accuracy at the same time. In this case, it is necessary for complex structures to construct damping matrix that damping ratios in more than two modes are equal to the accurate values.

关 键 词：地震反应 Rayleigh阻尼 加权最小二乘法 优化分析 穹顶结构 

分 类 号：TU311.3[建筑科学—结构工程] TU352.11