动力机器基础振动的Lysmer理论法与有限元法的对比研究
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摘要
采用有限元数值方法与理论计算法的对比研究,提出了一种验证动力机器基础Lysmer理论适用性的分析方法。首先根据二阶常系数非齐次微分方程理论,推求得到Lysmer方程的理论解,建立了动力基础的理论模型和相同条件下有限元数值试验模型,并分别采用有限元数值计算和理论计算得到在相同外周期动荷载作用下两种模型的位移历时曲线。计算结果发现,两种位移历时曲线的总体形状、初始相位和振动频率均非常接近,振幅之间存在明显的线性关系,反映出两者之间具有良好的可比性。
An adaptable analysis method for testing Lysmer theory of dynamic machine foundation is suggested using the comparative research algorithm of FEM numerical method and theoretical computation method in this paper.The theoretical solution to Lysmer equation is deduced based on the non-homogeneous differential equation theory of the second-order constant coefficient,and then the theoretical model for vibration of dynamic machine foundation and the finite element numerical model under the same condition are built.The two displacement curves of the models under the moving loading action in the same outside cycle have been calculated and obtained respectively.It has been found via the calculation results that total shape,initial phase and vibration frequency of displacement time intervals of two kinds are very close and that there exists an obvious linear relationship among the vibration frequencies,whereby reflecting that there is a better comparison between the both.
An adaptable analysis method for testing Lysmer theory of dynamic machine foundation is suggested using the comparative research algorithm of FEM numerical method and theoretical computation method in this paper.The theoretical solution to Lysmer equation is deduced based on the non-homogeneous differential equation theory of the second-order constant coefficient,and then the theoretical model for vibration of dynamic machine foundation and the finite element numerical model under the same condition are built.The two displacement curves of the models under the moving loading action in the same outside cycle have been calculated and obtained respectively.It has been found via the calculation results that total shape,initial phase and vibration frequency of displacement time intervals of two kinds are very close and that there exists an obvious linear relationship among the vibration frequencies,whereby reflecting that there is a better comparison between the both.
引文
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[5]王宏伟,陈啸,刘斌,等.动力基础频变参数模型及设计[J].建筑科学与工程,2008,25(1):55-59.Wang Hongwei,Chen Xiao,Liu Bin,et al.Frequencyvariable parameters model and design of dynamic founda-tions[J].Journal of Architecture and Civil Engineering,2008,25(1):55-59.
[6]蒋东旗,谢定义.动力机器基础设计的数值方法研究[J].土木工程学报,2002,35(1):74-78.Jiang Dongqi,Xie Dingyi.Numerical simulation method forfoundation design of dynamic machine[J].China Civil En-gineering Journal,2002,35(1):74-78.
[7]Chen Shishuenn,Shi Junyang.Simplified model for verticalvibrations of surface foundations[J].Journal of Geotechni-cal and Geoenvironmental Engineering,2006,132(5):651-655.
[8]Pradhan P K,Mandal A,Baidya D K,et al.Dynamic re-sponse of machine foundation on layered soil[J].Geotech-nical and Geological Engineering,2008,26(4):453-468.
[9]Li Ning.Wave Propagation Problems in the Jointed RockMass[M].Xi’an:Press of Northwest University of Tech-nology,1993.
[10]谢定义.土动力学[M].西安:西安交通大学出版社,1988.
[11]廖振鹏.工程波动理论导引[M].北京:科学出版社,1996.
[12]简政,杨芳,李爱国.相邻机器基础动力相互作用研究[J].西安理工大学学报,2006,22(3):265-268.Jian Zheng,Yang Fang,Li Aiguo.Research on dynamicinteraction between adjacent machine foundations[J].Journal of Xi’an University of Technology,2006,22(3):265-268.
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