振型叠加法合理振型数目的确定  

Determination of reasonable mode number for mode superposition approach

作　　者：陈华霆 谭平[1] 和雪峰[1] 彭凌云[2] 周福霖[1] 

机构地区：[1]广州大学工程抗震研究中心,广州510405 [2]北京工业大学建筑工程学院,北京100022

出　　处：《应用力学学报》2017年第3期404-409,共6页Chinese Journal of Applied Mechanics

基　　金：长江学者和创新团队发展计划(IRT13057)

摘　　要：振型叠加法是常用的动力时程分析方法之一,参与计算的振型数目是影响该方法精度的重要因素。本文揭示了确定振型参与数目的质量参与系数法、振型位移控制法的数学背景及物理含义,分析了两者存在的不足。通过推导振型截断误差估计公式,提出了更合理的确定振型数目范数形式的方法。这种方法基于严密的理论推导,适用于任意动力荷载形式。计算结果表明,振型位移控制法所确定的振型数目过大,质量参与系数法提供的振型数目偏少,而本文方法更有优势。Mode superposition approach is one of common dynamic analysis methods,in which the number of modes involved in the approach has significant effects on the calculation results.The mathematical backgrounds and physical meanings of participation mass ratio method and displacement control method are revealed in this paper and their deficiencies are indicated.Based on the errors of modal truncation,a new measure called norm method to determinate reasonable mode numbers is put forward,which has a rigorous theoretical base and is suitable to any form of dynamic load.A numerical example shows that the proposed method is more reasonable and effective,while the mode number determined by the participation mass ratio method is fewer and that by the displacement control method is too conservative.

关 键 词：动力分析 振型叠加 质量参与系数法 振型位移控制法 范数方法 

分 类 号：TU311.3[建筑科学—结构工程]