三维黏弹性介质人工边界研究
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摘要
为了得到适于分析非线性结构-地基相互作用问题的人工边界,结合弹性波理论与黏弹性理论,推导出了适于模拟三维黏弹性远场介质辐射阻尼的人工边界,并对其模拟远场地基辐射阻尼的性能及相应地震波动输入方法进行了研究。结果表明:在结构-地基动力相互作用问题中,得到的黏弹性人工边界模拟计算域外远场黏弹性介质的辐射阻尼具有理想精度;不论是简谐波还是非简谐波,地震波动输入都取得了理想结果;在黏弹性介质条件下自由地表处的总场位移幅值n是输入波幅值的2e-αx倍。
In order to get the artificial boundary that suits to analyze nonlinear structure-foundation interaction problems, the viscoelastic artificial boundary simulating radiation damping of the far field medium was obtained from the elastic wave theory and viscoelasticity theory. The ability of viscoelastic artificial boundary to simulate radiation damping and methods of seismic wave motion input were studied. The results show good precision when simulating radiation damping of far fields with the viscoelastic artificial boundary obtained from this paper in solving structure-foundation interaction problems. Precise results can be obtained through seismic wave motion input methods obtained in this paper whether the input wave is simple harmonic one or simple nonharmonic one. The displacement peak value at the free earth surface is n = 2e -αx times as high as that of input wave in viscoelastic medium.
In order to get the artificial boundary that suits to analyze nonlinear structure-foundation interaction problems, the viscoelastic artificial boundary simulating radiation damping of the far field medium was obtained from the elastic wave theory and viscoelasticity theory. The ability of viscoelastic artificial boundary to simulate radiation damping and methods of seismic wave motion input were studied. The results show good precision when simulating radiation damping of far fields with the viscoelastic artificial boundary obtained from this paper in solving structure-foundation interaction problems. Precise results can be obtained through seismic wave motion input methods obtained in this paper whether the input wave is simple harmonic one or simple nonharmonic one. The displacement peak value at the free earth surface is n = 2e -αx times as high as that of input wave in viscoelastic medium.
引文
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[2]刘晶波,王振宇,杜修力,等.波动问题中的三维时域黏弹性人工边界[J].工程力学,2005,22(6):46-51.LIU Jing-bo,WANG Zhen-yu,DU Xiu-li,et al.Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46-51.
[3]LYSMER J,KULEMEYER R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics Division(ASCE),1969,95(4):859-877.
[4]CLAYTON R,ENGQUIST B.Absorbing boundary conditions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,76(2):1529-1540.
[5]廖振鹏,黄孔亮,杨柏坡,等.暂态波透射边界[J].中国科学(A辑),1984,26(6):50-56.LIAO Zhen-peng,HUANG Kong-liang,YANG Bai-po,et al.Transient wave transmitting boundary[J].Science inChina(Ser.A),1984,26(6):50-56.
[6]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,1994,120(1):25-42.
[7]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55-64.LIU Jing-bo,LüYan-dong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55-64.
[8]王振宇,刘晶波.成层地基非线形波动问题人工边界与波动输入研究[J].岩石力学与工程学报,2004,23(7):1169-1173.WANG Zhen-yu,LIU Jing-bo.Study on wave motion input and artificial boundary for problem of nonlinear wave motion in layered soil[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(7):1169-1173.
[9]周光泉,刘孝敏.黏弹性理论[M].合肥:中国科学技术大学出版社,1996.
[10]刘汉龙,高玉峰,朱伟,等.边界条件对土层黏弹性地震反应的影响[J].岩土力学,2001,22(4):408-412.LIU Han-long,GAO Yu-feng,ZHU Wei,et al.Influences of boundary condition on the visco-elastic seismic response of soil layer[J].Rock and Soil Mechanics,2001,22(4):408-412.
[11]AKI K,RICHARDS P G.Quantitative seismology theory and methods[M].San Francisco:W H Freeman and Company,1980.
[12]张相庭.结构振动力学[M].上海:同济大学出版社,2005.
[13]廖振鹏.工程波动理论导论[M].北京:科学出版社,2003.
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