回传射线矩阵法分析桩的横向动力响应
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摘要
将Timoshenko梁引入到弹性地基梁模型中 ,考虑地基土的分层变化 ,建立了桩顶作用一水平动荷载桩的横向动力响应的基本方程。采用Fourier变换和回传射线矩阵法 ,获得了桩基横向自由振动的频率方程 ;通过离散Fourier反变换 ,得到了冲击荷载作用下桩身的动力响应。经算例分析 ,桩基横向动力响应的传播深度与土层分布以及桩土之间的相对刚度密切相关
In this paper, Timoshenko beam on elastic foundation is introduced to model a pile in a layered half space under a dynamic lateral loading. The wave equation of the system in frequency domain is established using Fourier transform. The natural frequency equation and dynamic response of the system are also obtained using the method of reverberation ray matrix. And then, the response of a pile under transient loading is presented by means of the discrete Fourier inverse transform. Case studies show that the dynamic response of a pile is closely related with the distribution of layered soil and the relative stiffness between pile and soil.
In this paper, Timoshenko beam on elastic foundation is introduced to model a pile in a layered half space under a dynamic lateral loading. The wave equation of the system in frequency domain is established using Fourier transform. The natural frequency equation and dynamic response of the system are also obtained using the method of reverberation ray matrix. And then, the response of a pile under transient loading is presented by means of the discrete Fourier inverse transform. Case studies show that the dynamic response of a pile is closely related with the distribution of layered soil and the relative stiffness between pile and soil.
引文
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[2]ReeseLC ,WelchRC .Lateralloadingsofdeepfoundationsinstiffclay[J].JGeotechEngrgDiv,ASCE ,1975,101(7):633-649.
[3]SunK .Laterallyloadedpilesinelasticmedia[J ].JGeotech EngrgDiv,ASCE ,1994,120(8):1324-1344.
[4]VerruijtA ,KooijmanAP .Laterallyloadedpilesinalayerede lasticmedium[J].Geotechnique,1989,39(1):39-46.
[5]ZhangLianyan,HerbertHEinstein.Nonlinearanalysisoflaterallyloadedrock socketedshafts[J].JournalofGeotehnicalandGeoenvironmentalEngineering,ASCE ,2000,126(11):955-968.
[6]OsmanIGhazzaly,SamTHwong,MichaelWO’Nell.Ap proximateanalysisofapileunderdynamiclateralloading[J].Computer&Structure,1976,6:363-368.
[7]FloresBerronesRaul,RobertVWhitman.Seismicresponseofend bearingpiles[J].JGeotechEngrgDiv,ASCE ,1982,108(4):554-569.
[8]刘宗贤,李玉亭.桩基础在阻尼与分层弹性地基场地土波动影响下的横向地震反应分析[J].地震工程与工程振动,1994,14(3):47-59.
[9]YinJianhua.Closed formsolutionforreinforcedTimoshenkobeamonelasticfoundation[J].JournalofEngineeringMechan ics,2000,126(8):868-874.
[10]YinJianhua.Comparativemodelingstudyonreinforcedbeamonelasticfoundation[J].JournalofGeotechnicalandGeoenviron mentalEngineering,ASCE ,2000,126(3):265-271.
[11]HowardSM ,PaoYH .Analysisandexperimentsonstresswavesinplanartrusses[J].JournalofEngineeringMechanics,1998,124(8):884-891.
[12]PaoYH ,KehDC .Dynamicresponseandwavepropagationinplanetrussesandframes[J].AIAAJournal,1999,37(5):594-603.
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