振型降阶法解决被动控制中小刚度引起的病态问题  

Reduction of the number of equations by mode-superposition for solving the illness

作　　者：田志昌[1] 张瑞雪 Tian Zhichang;Zhang Ruixue(Inner Mongolia University of Science and Technology,014010,Baotou,China)

机构地区：[1]内蒙古科技大学,包头014010

出　　处：《应用力学学报》2018年第6期1295-1299,1422,共6页Chinese Journal of Applied Mechanics

基　　金：包头市科技计划项目(2013J2001-2)

摘　　要：被动控制系统调谐质量阻尼器(Tuned Mass Damper,TMD)或调谐液体阻尼器(Tuned Liquid Damper,TLD)刚度相对主体结构非常小,而且通常是非线性的,所以动力时程计算中极易出现病态刚度矩阵。当主体结构未知量个数相当大时,刚度矩阵的病态很难避免。为了使病态方程得到改善,本文利用主体结构振型叠加法降低方程阶数。在完成降阶后,根据Newmark-β法推导了计算地震作用下每一时刻结构响应的公式,并将整个算法使用MATLAB编译为程序。通过与已有文献中ABAQUS模拟结果的对比,得出误差在2.9%～8.4%范围内,说明本算法可以提高计算效率,具有较高的精确度。The stiffness of a passive control system,e.g.Tuned Mass Damper (TMD)or Tuned Liquid Damper (TLD),is very small and nonlinear,which often causes the stiffness matrix to be ill-condition state in dynamic analysis.This illness could rarely be avoided if the number of unknown quantity of main body structure is large.A method is presented in this paper by using mode-superposition method to reduce the number of equations to improve the illness.After the completion of the reduction order,according to the basic principle of Newmark-β method,the formula for calculating the response of each moment under the action of earthquake is deduced,and the whole algorithm is compiled into MATLAB software.By comparing with the results by ABAQUS simulation reported in the previous literature,this algorithm can improve the computational efficiency and has high accuracy. The error rate is about in 2.9%-8.4%.

关 键 词：TMD TLD 刚度矩阵 振型叠加法 降阶 

分 类 号：TU311[建筑科学—结构工程]