结构-地基相互作用水平与扭转的超亚谐振动
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摘要
基于多线性随动强化模型求得了基础和地基土之间的水平刚度与摇摆刚度,在此基础上建立了结构-地基非线性相互作用体系模型,利用能量法得到了结构水平侧移和扭转相耦合的振动方程,采用多尺度法研究了结构-地基相互作用体系的超谐和亚谐共振,比较了结构与地基非线性因素给体系反应带来的影响,揭示了发生超谐和亚谐振动时水平振动和扭转振动耦合的不同规律,为工程抗震提供了理论依据。
In the paper,based on the multilinear kinematic hardening mode,the nonlinear finite element method is applied to obtain the relationship between horizontal load and displacement of foundation and the relationship between moment and rock angle of foundation.And then a model of soil-structure spatial nonlinear interaction system is derived and the nonlinear coupling equation of horizontal motion and torsion motion is given as the result of the application of the Lagrange energy equation.The superharmonic resonance and subharmonic resonance behavior of soil-structure interaction system are studied via perturbation method.A comparison upon the responses of the systems with structure-soil nonlinear factors is presented,which explains the different coupling laws of horizontal motion and torsion motion when the superharmonic resonance and subharmonic resonance happen.The results given in this paper offer a theoretical foundation for the researches on engineering anti-seism.
In the paper,based on the multilinear kinematic hardening mode,the nonlinear finite element method is applied to obtain the relationship between horizontal load and displacement of foundation and the relationship between moment and rock angle of foundation.And then a model of soil-structure spatial nonlinear interaction system is derived and the nonlinear coupling equation of horizontal motion and torsion motion is given as the result of the application of the Lagrange energy equation.The superharmonic resonance and subharmonic resonance behavior of soil-structure interaction system are studied via perturbation method.A comparison upon the responses of the systems with structure-soil nonlinear factors is presented,which explains the different coupling laws of horizontal motion and torsion motion when the superharmonic resonance and subharmonic resonance happen.The results given in this paper offer a theoretical foundation for the researches on engineering anti-seism.
引文
[1]谷岩,姜忻良.地基-非线性结构相互作用体系的超谐和亚谐共振[J].地震工程与工程振动,2001,21(1):56—60.
[2]姜忻良,骆兰月.考虑非对称效应的非线性结构超谐共振与亚谐共振[J].地震工程与工程振动,2003,23(6):50—56.
[3]Pe llicano F,V estron i F.N on linear dynam ics and b ifur-cations of an ax ia lly m ov ing beam s[J].Journa l of v i-bration and A coustics,2000,122(1):21—30.
[4]W ang Y M.T he dynam ic ana lys is of a beam-m ass sys-tem due to the occurrence of tw o-com ponen t param et-ric resonance[J].Journa l of Sound and V ibration,2002,258(5):951—967.
[5]M accari A.V ibration con tro l for the prim ary reso-nance of a can tilever bean by a tim e de lay state feed-back[J].Journa l of Sound and V ibration,2003,259(2):241—251.
[6]Popov A A.Param etric resonance in cy lindrica l she lls:a case study in the non linear v ibration of structura lshe lls[J].Eng ineering S tructures,2003,25(5):789—799.
[7]H euer R and Z ieg ler F.N on linear resonance phenom e-na of pane l-type structures[J].Com pu ters and S truc-tures,1998,67(1):65—70.
[8]C a i Y X,G ou ld P L,D esa i C S.N on linear ana lys is of3D se ism ic in teraction of so il-p ile-structure system sand app lication[J].Eng ineering S tructures,2000,22(2):191—199
[2]姜忻良,骆兰月.考虑非对称效应的非线性结构超谐共振与亚谐共振[J].地震工程与工程振动,2003,23(6):50—56.
[3]Pe llicano F,V estron i F.N on linear dynam ics and b ifur-cations of an ax ia lly m ov ing beam s[J].Journa l of v i-bration and A coustics,2000,122(1):21—30.
[4]W ang Y M.T he dynam ic ana lys is of a beam-m ass sys-tem due to the occurrence of tw o-com ponen t param et-ric resonance[J].Journa l of Sound and V ibration,2002,258(5):951—967.
[5]M accari A.V ibration con tro l for the prim ary reso-nance of a can tilever bean by a tim e de lay state feed-back[J].Journa l of Sound and V ibration,2003,259(2):241—251.
[6]Popov A A.Param etric resonance in cy lindrica l she lls:a case study in the non linear v ibration of structura lshe lls[J].Eng ineering S tructures,2003,25(5):789—799.
[7]H euer R and Z ieg ler F.N on linear resonance phenom e-na of pane l-type structures[J].Com pu ters and S truc-tures,1998,67(1):65—70.
[8]C a i Y X,G ou ld P L,D esa i C S.N on linear ana lys is of3D se ism ic in teraction of so il-p ile-structure system sand app lication[J].Eng ineering S tructures,2000,22(2):191—199
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