波谱单元法在空间桁架地震响应分析中的应用  

Application of spectral element method in dynamic analysis of a space truss subjected to seismic load

作　　者：张俊兵[1,2] 朱宏平[1,2] 王丹生[1,2] 閤东东[1,2] 

机构地区：[1]华中科技大学土木工程与力学学院,武汉430074 [2]华中科技大学控制结构湖北省重点实验室,武汉430074

出　　处：《振动与冲击》2011年第5期245-251,共7页Journal of Vibration and Shock

基　　金：国家杰出青年基金(50925828);国家自然科学基金资助项目(50778077);高校博士学科点专项科研基金(20070487099)

摘　　要：针对传统波谱单元法(SEM)只能用于求解节点集中荷载作用下结构动力响应问题的不足,提出了一种通过计算地震等效波谱节点荷载求解桁架结构地震响应的方法。基于虚功原理,利用波谱形函数积分得到地震等效波谱节点荷载的显式表达式,通过修改波谱单元法中单元刚度矩阵的波数,考虑了阻尼对结构动力特征的影响,采用数值拉普拉斯(Laplace)变换替换快速傅里叶(FFT)变换,回避了传统波谱单元法中FFT的周期性问题。利用地震荷载等效后的波谱节点荷载对三维空间桁架结构进行地震响应分析,结果表明,采用本文的方法能方便的计算桁架结构的地震等效波谱节点荷载,精确求解结构的地震响应,与传统有限元法(FEM)相比,大大减少计算单元数量,提高计算精度,且便于编程计算。An extended spectral element method（SEM） was established to get dynamic responses of a space truss subjected to seismic load.The seismic load was equivalent to concentrated node forces by integrating the shape function in SEM based on the principle of virtual work.Both internal viscoelastic damping and external viscous damping of the truss bar were considered by just simply modifying the wave number.Laplace transformation instead of fast Fourier transformation（FFT） was utilized in SEM to avoid the periodicity of FFT.To evaluate the accuracy of Laplace-based SEM,the dynamic responses of a space truss under seismic load was analyzed as a numerical example.The numerical results obtained using FEM were compared with those using SEM.It was found that SEM provides good dynamic results under seismic load;the equivalent seismic node forces are convenient to get by programming calculation;SEM is proved to be an efficient method to analyze dynamic responses of structures accurately while the number of element greatly decreases.

关 键 词：波谱单元法 阻尼 波数 桁架 有限元 地震响应 

分 类 号：TU311.3[建筑科学—结构工程] TU323.4