层状土层随机地震反应分析的近似解法
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摘要
基于模态摄动方法,提出了层状土层随机地震反应的近似分析方法。该方法首先利用等效均匀剪切梁的模态和频率,将层状土层的微分方程转化为代数方程,得到层状土层的固有频率和模态。在此基础上,推导了层状土层随机地震反应的计算公式。最后通过算例,阐述了基于模态摄动法进行随机地震反应的计算过程并分析了该方法的计算误差。计算结果表明,这一方法简单有效,其误差可控制在5%以内。
Based on modal perturbation method, a new approach is developed for solving the random seismic response of horizontal layered soil. In the approach, the dynamic characteristics of layered soil are calculated approximately in the modal subspace spanned by several lower models of equivalent homogeneous shear beam with the same depth, average shear modulus and mass density. As a result, the differential vibration equation of soil layer with variable properties is transferred as a set of algebraic equations. Then the equation of random seismic response of layered soil is derived. By way of numerical example, the procedure and calculation error of random seismic response by using mode perturbation is discussed. Numerical results show that the approach is simple and practicable, that error is less than 5%.
Based on modal perturbation method, a new approach is developed for solving the random seismic response of horizontal layered soil. In the approach, the dynamic characteristics of layered soil are calculated approximately in the modal subspace spanned by several lower models of equivalent homogeneous shear beam with the same depth, average shear modulus and mass density. As a result, the differential vibration equation of soil layer with variable properties is transferred as a set of algebraic equations. Then the equation of random seismic response of layered soil is derived. By way of numerical example, the procedure and calculation error of random seismic response by using mode perturbation is discussed. Numerical results show that the approach is simple and practicable, that error is less than 5%.
引文
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[2]Dobry R,Oweis I,Uraua A.Simplified procedures for estimating the fundamental period of soil profile[J].Bulletin of Seismological Society of America,1979,66(4):1293―1321.
[3]Zhong W X,Lin J H,Gao Q.The precise computation for wave propagation in stratified materials[J].InternationalJournal for Numerical Methods in Engineering,2004,60(1):11―25.
[4]栾茂田,金崇磐,林皋.非均质地基振动特性及地震反应分析[J].大连理工大学学报,1992,32(1):81―87.Luan Maotian,Jin Chongpan,Lin Gao.Vibration behaviour and seismic response of vertically non-homogeneous soil deposits[J].Journal of Dalian University of Technology,1992,32(1):81―87.(in Chinese)
[5]楼梦麟.变参数土层的动力特性和地震反应分析[J].同济大学学报,1997,25(2):155―160.Lou Menglin.Dynamic analysis for modal characteristics and seismic response of soil layer with variable properties[J].Journal of Tongji University,1997,25(2):155―160.(in Chinese)
[6]栾茂田,刘占阁.成层场地振动特性及地震反应简化解析解的完整形式[J].岩土工程学报,2003,25(6):747―749.Luan Maotian,Liu Zhan’ge.A complete form of simplified analytical solution of natural vibration characteristics and seismic response of horizontally-layered soil sites[J].Chinese Journal of Geotechnical Engineering,2003,25(6):747―749.(in Chinese)
[7]胡聿贤.地震工程学[M].北京:地震出版社,1988.Hu Yuxian.Earthquake engineering[M].Beijing:Earthquake Press,1988.(in Chinese)
[8]吴再光,林皋,韩国成.水平成层地基非平稳随机地震反应分析[J].土木工程学报,1992,25(3):60―67.Wu Zaiguang,Lin Gao,Han Guocheng.Nonstationary stochastic seismic response analysis of horizontal layered foundations[J].China Civil Engineering Journal,1992,25(3):60―67.(in Chinese)
[9]曾心传,秦小军.土层对地震的随机反应分析[J].地震工程与工程振动,1998,18(3):27―39.Zeng Xinchuan,Qin Xiaojun.Analysis of random response of soil layer to earthquake[J].Earthquake Engineering and Engineering Vibration,1998,18(3):27―39.(in Chinese)
[10]黄义,王春玲,曹彩芹.成层地基一维土层对地震的随机反应分析[J].世界地震工程,2004,20(1):126―132.Huang Yi,Wang Chunling,Cao Caiqin.Random response analysis of stratified foundations to earthquakes[J].World Earthquake Engineering,2004,20(1):126―132.(in Chinese)
[11]潘旦光,楼梦麟,董聪.SH波作用下层状土层随机波动分析[J].工程力学,2005,22(5):20―25.Pan Danguang,Lou Menglin,Dong Cong.Random wave-theory analysis of layered soil sites under SH wave excitation[J].Engineering Mechanics,2005,22(5):20―25.(in Chinese)
[12]朱位秋.随机振动[M].北京:科学出版社,1998.Zhu Weiqiu.Random vibration[M].Beijing:Science Press,1998.(in Chinese)
[13]楼梦麟,吴京宁.复杂梁动力问题的近似分析方法[J].上海力学,1997,18(3):234―240.Lou Menglin,Wu Jingning.An approach to solve dynamic problems of complicated beams[J].Shanghai Journal of Mechanics,1997,18(3):234―240.(in Chinese)
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