弹性结构与晃动液体耦合系统的动力特性分析
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摘要
基于弹性波传播理论,构造液体晃动的等效弹性体模型,将液体晃动问题归结为弹性体动力问题,建立位移-压力格式的流固耦合方程,采用静态缩聚技术求解流固耦合特征值问题。在此基础上,推导地震条件下的流固耦合系统有限元模型。对储液容器的特征值问题和动态响应问题进行了实例分析和计算,算例结果验证了方法的正确性与有效性。
Based on elastic wave propagation theory,the equivalent elastic body for liquid sloshing was obtained and the liquid sloshing can be formulated as a dynamic question for elastic body.The 3-D liquid-filled tank was considered as a fluid-structures interaction system that consists of the ideal fluid with free surface and the linear,elastic solid with thin thickness,and the coupling equation based on displacement(structure)-pressure(fluid with free surface) format was established.The static condensation method was used for eigenvalue problems of liquid sloshing.Taking into account earthquake effect leads to additional load to the coupling equations,a finite element model of liquid-filled tank was set up.The eigenvalue problem and dynamic response of a liquid-filled tank were studied using the model.A numerical simulation of a liquid-filled tank was carried out to confirm the validity and effectiveness of the method.
Based on elastic wave propagation theory,the equivalent elastic body for liquid sloshing was obtained and the liquid sloshing can be formulated as a dynamic question for elastic body.The 3-D liquid-filled tank was considered as a fluid-structures interaction system that consists of the ideal fluid with free surface and the linear,elastic solid with thin thickness,and the coupling equation based on displacement(structure)-pressure(fluid with free surface) format was established.The static condensation method was used for eigenvalue problems of liquid sloshing.Taking into account earthquake effect leads to additional load to the coupling equations,a finite element model of liquid-filled tank was set up.The eigenvalue problem and dynamic response of a liquid-filled tank were studied using the model.A numerical simulation of a liquid-filled tank was carried out to confirm the validity and effectiveness of the method.
引文
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[2]SEZEN H,LIVAOGLU R,DOGANGUN A.Dynamic a-nalysis and seismic performance evaluation of above-ground liquid-containing tanks[J].Engineering Struc-tures,2008(30):794-803.
[3]王照林,刘延柱.充液系统动力学[M].北京:科学出版社,2002.
[4]LIU Dong-ming,LIN Peng-zhi.A numerical study ofthree-dimensional liquid sloshing in tanks[J].Journalof Computational Physics,2008(227):3921-3939.
[5]MITRA S,SINHAMAHAPATRA K P.2D simulation offluid-structure interaction using finite element method[J].Finite Elements in Analysis and Design,2008(45):52-59.
[6]李遇春,楼梦麟.渡槽中流体非线性晃动的边界元模拟[J].地震工程与工程振动,2000,20(2):51-56.LI Yu-chun,LOUMeng-lin.BEMsimulation of nonlinearsloshing for aqueduct fluid[J].Earthquake Engineeringand Engineering Vibration,2000,20(2):51-56.
[7]岳宝增,刘延柱.带自由液面Navier-Stokes流动问题的ALE分步有限元方法[J].水动力学研究与进展,2003,18(4):463-469.YUE Bao-zeng,LIUYan-zhu.ALE finite element methodfor free surface Navier-Stokes flow using fractional stepmethods[J].Journal of Hydrodynamics,2003,18(4):463-469.
[8]杜建镔,王勖成.旋转周期性含液容器的流固耦合动力特性分析[J].清华大学学报,1999,39(8):108-111.DU Jian-bin,WANG Xu-cheng.Fluid structure couplingdynamic characteristic analysis for rotationally periodicliquid filled vessel[J].Journal of Tsinghua University,1999,39(8):108-111.
[9]李彦民,徐刚,任文敏,等.储液容器流固耦合动力响应分析计算[J].工程力学,2002,19(4):29-31.LI Yan-min,XU Gang,REN Wen-min,et al.Dynamicresponse analysis of liquid-filled tanks[J].EngineeringMechanics,2002,19(4):29-31.
[10]徐刚,任文敏,张维,等.储液容器的三维流固耦合动力特性分析[J].力学学报,2004,36(3):328-334.XU Gang,RENWen-min,ZHANG Wei,et al.Dynam-ic characteristic analysis of liquid-filled tanks as a 3-Dfluid-structure coupling system[J].Acta MechanicaSinica,2004,36(3):328-334.
[11]吴家龙.弹性力学[M].北京:高等教育出版社,2001.
[12]赵玉成,张亚红,白长青,等.固体火箭发动机模态分析的缩聚方法[J].固体火箭技术,2004,27(2):98-100.ZHAO Yu-cheng,ZHANG Ya-hong,BAI Chang-qing,et al.Modal analysis of solid rocket motors by means ofa reduced method[J].Journal of Solid Rocket Technol-ogy,2004,27(2):98-100.
[13]朱安文,曲广吉,高耀南.航天器结构动力模型修正中的缩聚方法[J].中国空间科学技术,2003(2):6-10.ZHU An-wen,QU Guang-ji,GAO Yao-nan.Matrix re-duction method for updating dynamic model[J].Chi-nese Space Science and Technology,2003(2):6-10.
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