一般非对称非经典结构响应的二阶实振子精确解耦法  

Exact decoupling method of general asymmetric and non-classical structure in second-order real oscillatory vibration

作　　者：李创第[1] 葛新广[1] 邹万杰[1] 李暾[1] 陈欧阳[2] 

机构地区：[1]广西科技大学土建学院,柳州545006 [2]广西大学土建学院,南宁530004

出　　处：《应用力学学报》2014年第2期212-217,308-309,共6页Chinese Journal of Applied Mechanics

基　　金：广西高校百名中青年学科带头人资助计划(RC20060814017)

摘　　要：为使现代一般非对称非经典结构的分析和设计法等同于基于物理意义明确的二阶标准振子传统经典结构,对该类结构响应的二阶标准实振子精确解耦法进行了系统研究。首先,运用复模态法对具有一般非对称质量和刚度矩阵及非对称非经典阻尼矩阵结构的响应进行精确解耦;其次,构造复响应量与实响应量的变换关系,运用拉氏变换,通过实矩阵坐标变换法,将一般非对称非经典结构及被动减震结构的位移与速度响应精确解耦为系列二阶标准实振子位移与速度响应及地震位移与速度响应的线性组合,并使系列标准振子的广义荷载仅为原始荷载的实数线性组合;最后,对实振子与实模态解耦法进行了对比分析。结果表明:实模态解耦法是实振子解耦法的特殊情况;当一般非对称非经典结构退化为经典结构时,实矩阵坐标变换法退化为实模态坐标变换法,实振子解耦法退化为实模态解耦法。此外,运用本文所建立的方法,可将现有的成熟经典结构体系的分析与设计法直接推广到一般非对称非经典复杂结构体系。In order to equalize the analytical and design methods of general asymmetric and non-classicalstructure to those of classical structure, the exact decoupling method of general asymmetric and non-classical structure in second-order real oscillatory vibration is studied systematically. Firstly, the structural dynamic equations with general non-classical damping and asymmetric mass and stiffness matrix are decoupled exactly by complex mode method. Then, by constructing transformation of complex and real response, using Laplace Transform and real matrix coordinate transformation, the exact decoupling method of general asymmetric and non-classical structure in second-order real oscillatory vibration is established, the displacement and velocity response of general asymmetric and non-classical structure are exactly decomposed to linear combination of displacement and velocity response of serial second-order standard real oscillators. The general loads of serial standard oscillators are real linear combination of original structural loads, the displacement and velocity response of general asymmetric and non-classical structure seismic retrofitting also can be exactly decomposed in the same way. Finally, the decoupling methods in real oscillatory vibration and in real mode are compared. It is demonstrated that the decoupling method in real mode is the special case of that in real oscillatory vibration. It is also indicated that when the general asymmetric and non-classical structure degenerates into the symmetric and classical structure, the real matrix coordinate transformation degenerates into real mode coordinate transformation, the decoupling method in real oscillatory vibration degenerates into that in real mode. Therefore, by using above decoupling method in real oscillatory vibration, the existing effective analytical and design methods of classical structure can be directly extended to general asymmetric and non-classical structure.

关 键 词：非对称非经典结构 被动减震结构 实矩阵坐标变换法 实振子解耦法 实模态解耦法 标准振子振动分解 

分 类 号：TU313.3[建筑科学—结构工程]