第一作者李永华男，博士，副教授，1972年生

通信作者桂国庆男，博士，教授，1966年生

绝对位移直接求解虚拟激励法采用附加振型求解的理论研究

李永华1，桂国庆2,1，廖宇1

(1.南昌大学建筑工程学院，南昌330031； 2.井冈山大学建筑工程学院，江西吉安343009)

摘要：为提高已有绝对位移直接求解虚拟激励法的求解效率及精度，对结构支座节点附加大质量块并释放支座约束，采用基于附加振型的振型分解法进行求解，附加振型来源于附加大质量块。对附加振型、常规振型的振型特性和振型贡献及计算效率进行了理论分析，分析表明：通过构建少量附加振型就可精确捕获结构拟静位移，且只需采用与相对运动法同等数量的常规振型就可精确捕获结构动态相对位移，与Wilson位移输入模式的绝对位移振型分解法相比，在保证计算精度的条件下可大大减少绝对位移求解所需的振型数。此外，对附加振型绝对位移求解法阻尼误差进行了理论分析，指出了附加振型法不存在由于阻尼假定不同而引起的误差，计算精度及效率均优于基于完全法的绝对位移直接求解法。

关键词：附加振型；虚拟激励法；绝对位移直接求解；振型分解；误差分析

基金项目：国家自然科学

收稿日期：2013-10-09修改稿收到日期：2014-04-30

中图分类号:TU311.3文献标志码：A

Pseudo excitation method based on directly solving absolute diaplacements with addtional modes

LIYong-hua1,GUIGuo-qing1,2,LIAOYu1(1.School of Architecture and Civil Engineering, Nanchang University, Nanchang 330031, China; 2. School of Architecture and Civil Engineering, Jinggangshan University, Ji’an 343009, China)

Abstract:Structures were solved using the pseudo excitation method with additional modes through adding big masses on support nodes in order to improve the calculation accuracy and efficiency of the old pseudo excitation method based on directly solving absolute displacements. The additional modes were caused by the added big masses. The contribution and characterisitics of additional modes and the conventional ones as well as the calculation efficiency of the new algorithm were analyzed. It was shown that constructing only few additional modes can capture the pseudo-static displacement responses of structures accurately, and adopting the same number of conventional modes obtained with the relative motion method can capture the same accurate dynamic relative displacement responses of structures; compared with the displacement input model presented by Wilson, the proposed method can lead to a significant reduction of the required modes for solving absolute displacements with the same accuracy; the calculation errors caused by different damping assumings don’t exist in the new algorithm, so it is superior to the old pseudo excitation method based on directly solving absolute displacements in accuracy and efficiency.

Key words:additional modes; pseudo excitation method; directly solving absolute displacement; mode decomposition; error analysis

李永华[1]提出了一种随机振动绝对位移直接求解的虚拟激励法，该方法通过在基底附加大质量块直接对绝对位移进行一次性求解，避免了在构建虚拟激励的过程中需提取整体结构质量和刚度矩阵的繁琐，且可在通用有限元软件中直接实现,大大方便了多点激励随机振动工程应用[2-4]，该算法已得到较好的应用和发展。……