弹性圆拱在非平稳水平随机地震作用下的伽辽金法
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摘要
应用虚拟激励法与伽辽金法相结合,分析弹性圆拱在非平稳水平随机地震作用下的随机响应问题.在建立圆拱动力平衡微分方程的基础上,通过选取适当的试函数,将动力平衡方程转化为线性常微分方程组.通过设定虚拟荷载,按确定性方法求解响应量的时变功率谱密度的近似解,并进一步求出响应的方差和各阶谱矩.由于采用较少的试函数就能获得较高的精度,大大提高了计算效率.
The nonstationary random response of elastic circular arch under horizontal seismic excitation was studied by the method combining the pseudo-excitation algorithm with Galerkin algorithm.On the basis of establishing the dynamical equilibrium differential equations of circular arch which can be transformed into system of linear ordinary differential equations by choosing appropriate trial functions,the approximate solution of evolutionary power spectrum density,variance and random spectral moment of response were solved by assuming pseudo-excitation load.The method is highly efficient owing to only using few trial functions.
The nonstationary random response of elastic circular arch under horizontal seismic excitation was studied by the method combining the pseudo-excitation algorithm with Galerkin algorithm.On the basis of establishing the dynamical equilibrium differential equations of circular arch which can be transformed into system of linear ordinary differential equations by choosing appropriate trial functions,the approximate solution of evolutionary power spectrum density,variance and random spectral moment of response were solved by assuming pseudo-excitation load.The method is highly efficient owing to only using few trial functions.
引文
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[2]N.C.尼格姆.随机振动概论[M].何成慧,译.上海:上海交通大学出版社,1985:139-155.
[3]向天宇,赵人达.大跨度拱在空间变化的非平稳随机地震动作用下的随机响应[J].中国公路学报,2001,14(1):39-41.XIANG Tian-yu,ZHAO Ren-da.Random response of long span arch under spatially variable seismic excitation[J].ChinaJournal of Highway and Transport,2001,14(1):39-41.(in Chinese)
[4]LIN Jia-hao,SONG Gui-zhen,SUN Yong,et al.Non-stationary random seismic responses of non-uniform beams[J].SoilDynamics and Earthquake Engineering,1995,14:301-306.
[5]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:60-80.
[6]项海帆,刘光栋.拱结构的稳定与振动[M].北京:人民交通出版社,1991:10.
[7]A.H.金尼克.拱的稳定性[M].吕子华,译.北京:建筑工程出版社,1958:13-20.
[8]Shinozuka M,Sato Y.Simulation of nonstationary random process[J].J Engrg Mech ASCE,1967,93(1):11-40.
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