结构体系的一种新型半解析动力算法——地下结构动力分析的拉普拉斯积分变换解法
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摘要
得到了地下结构在水平地震作用下的动力运动方程,利用拉普拉斯变换和结构的对接条件,得到了求解待定系数的超越方程。利用拉普拉斯逆变换得到了结构的位移表达式和确定拉普拉斯参数极点的方程。进一步研究发现,拉普拉斯变换参数s与结构频率ω之间存在某种特殊的关系:s2=?ω2。为了避免确定待定系数及拉普拉斯参数极点时求解复杂超越方程的困难,建议通过数值的办法先把结构体系的频率求出来,再通过拉普拉斯逆变换留数定理求解结构的位移和内力。
The dynamic motion equations of underground structure under horizontal seismic action are obtained. The transcendental equation for the determination of solution coefficients is deduced by using Laplace integral transform method and linking conditions of structure members. Using inverse Laplace integral transform method the equations for the determination of the displacements of the structure and the poles of the transformation parameters of the Laplace transform are obtained. The further study shows that a special relationship exists between the transformation parameters of Laplace transform s and natural frequency of structure ω : s 2 = ?ω 2. To avoid the difficulty in determining the coefficients of the solution and the poles of the transformation parameters of the Laplace transform in solving the transcendental equation, the authors suggest that the frequency of structural system is figured out firstly by numerical methods; then the structural displacement and internal forces are obtained by using the residue theorem of inverse Laplace transform.
The dynamic motion equations of underground structure under horizontal seismic action are obtained. The transcendental equation for the determination of solution coefficients is deduced by using Laplace integral transform method and linking conditions of structure members. Using inverse Laplace integral transform method the equations for the determination of the displacements of the structure and the poles of the transformation parameters of the Laplace transform are obtained. The further study shows that a special relationship exists between the transformation parameters of Laplace transform s and natural frequency of structure ω : s 2 = ?ω 2. To avoid the difficulty in determining the coefficients of the solution and the poles of the transformation parameters of the Laplace transform in solving the transcendental equation, the authors suggest that the frequency of structural system is figured out firstly by numerical methods; then the structural displacement and internal forces are obtained by using the residue theorem of inverse Laplace transform.
引文
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[2]川岛一彦.地下构筑物の耐震设计[M].[S.l.]:鹿岛出版会,1994.
[3]SHUKLA D K,RIZZO P C,STEPHENSON D E.Earthquake load analysis of tunnels and shafts[C]//Proceedings of the Seventh World Conference on Earthquake Engineering.[S.l.]:[s.n.],1980,8:201-208.
[4]JOHN C M ST,ZAHRAH T F.Aseismic design of underground structures[J].Tunneling and Underground Space Technology,1987,2(2):165-197.
[5]РАШИДОВ Т Р.Динамическая теория сейсмостой-кости сложных систем по-дземных сооружений[M].Ташкент:Фан,1973.
[6]РАШИДОВ Т Р.идругие.Сейсмостойкость тонне-льных конструкций метрополитенов[M].Москва:Транспорт,1975.
[7]国胜兵,赵毅,赵跃堂,等.地下结构在竖向和水平地震荷载作用下的动力分析[J].地下空间学报,2002,22(4):314-319.GUO Sheng-bing,ZHAO Yi,ZHAO Yue-tang,et al.Dynamic analysis of underground structures under the vertical and horizontal seismic load[J].Underground Space,2002,22(4):314-319.
[8]庄海洋,程绍革,陈国兴.阪神地震中大开地铁车站震害机制数值仿真分析[J].岩土力学,2008,29(1):246-250.ZHUANG Hai-yang,CHENG Shao-ge,CHEN Guo-xing.Numerical simulation and analysis of earthquake damages of Dakai metro station caused by Kobe earthquake[J].Rock and Soil Mechanics,2008,29(1):246-250.
[9]刘晶波,李彬,刘祥庆.地下结构抗震设计中的静力弹塑性分析方法[J].土木工程学报,2007,40(7):68-76.LIU Jing-bo,LI Bin,LIU Xiang-qing.A static elasto-plastic analysis method in seismic design of underground structures[J].China Civil Engineering Journal,2007,40(7):68-76.
[10]NAM S H,SONG H W,BYUN K J,et al.Seismic analysis of underground reinforced concrete structures considering elasto-plastic interface element with thickness[J].Engineering Structures,2006,28(8):1122-1131.
[11]彭俊生,罗永坤,彭地.结构动力学、抗震计算[M].成都:西南交通大学出版社,2007.
[12]龙驭球,包世华.结构力学教程(Ⅱ)[M].北京:高等教育出版社出版,2001.
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