求解Rayleigh阻尼系数的加权最小二乘法

发布时间：2018-01-19 22:41

本文关键词： 地震反应 Rayleigh阻尼加权最小二乘法优化分析位移反应谱　出处：《计算力学学报》2015年01期 　论文类型：期刊论文

【摘要】：在地震反应分析过程中,提出了一种优化方法以解决Rayleigh阻尼系数计算时选择两阶合理参考频率的难题。该方法是以反应谱理论为基础,以结构位移峰值误差最小为目标函数。将位移反应谱用一阶Taylor级数近似计算,从而将目标函数简化为加权最小二乘法的方程。随后以框架结构为例,讨论了模态个数和阻尼比模型对Rayleigh阻尼系数计算的影响,并与传统方法、最小二乘法及基于多参考振型的加权最小二乘法进行比较。计算结果表明,最小二乘法由于忽略了模态贡献的影响,不是计算Rayleigh阻尼系数的合理方法。当模态个数所包含的累积振型参与质量达90%以上,本文方法所得Rayleigh阻尼系数计算结果稳定,结构动力反应的计算精度高。
[Abstract]:In the process of seismic response analysis, an optimization method is proposed to solve the problem of selecting two order reasonable reference frequency in the calculation of Rayleigh damping coefficient, which is based on the theory of response spectrum. Taking the minimum displacement peak error as the objective function, the displacement response spectrum is approximately calculated by the first order Taylor series, and the objective function is simplified into the equation of the weighted least square method. Then, the frame structure is taken as an example. The influence of the number of modes and damping ratio model on the calculation of Rayleigh damping coefficient is discussed and compared with the traditional method. The least square method is compared with the weighted least square method based on multiple reference modes. The results show that the least square method neglects the influence of modal contribution. It is not a reasonable method to calculate the damping coefficient of Rayleigh. When the cumulative mode mass included in the number of modes is more than 90%. The calculated results of Rayleigh damping coefficient obtained by this method are stable and the calculation accuracy of structural dynamic response is high.
【作者单位】：北京科技大学土木工程系;
【基金】：国家自然科学基金(51078032)资助项目
【分类号】：TU311.3
【正文快照】： 1引言采用直接积分法进行结构动力反应计算时,必然涉及阻尼矩阵的计算[1]。由于阻尼的影响因素众多,且难以定量,因此,难以根据结构的几何尺寸和材料直接计算阻尼矩阵,而是采用构造的方法[2-4]。在阻尼矩阵的各种构造方法中,假定结构的阻尼矩阵是质量矩阵和刚度矩阵线性组合的R

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