群桩基础阻抗函数的集总参数模型研究
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摘要
利用改进后的Chebyshev多项分式进行复数拟合,得到群桩基础阻抗函数可扩展精度的集总参数模型,以获取时域分析和非线性分析的群桩基础参数。基于薄层法求解得到半无限地基中群桩基础的阻抗函数,利用改进的Chebyshev多项式的比值表示地基的动力柔度函数,将改进的Chebyshev多项分式表示成部分分式的形式,最后将其等效为两种基本类型的集总参数模型。通过与薄层法求解得到的地基动力刚度阻抗函数进行比较,给出的集总参数模型能在很宽的频段上与弹性半空间解吻合良好,得到的集总参数可以直接运用到群桩地基-结构相互作用的时域分析和非线性分析中。
The pile group impedance function was considered based on thin layer method,and attention was paid on the application of Chebyshev complex polynomials in the development of extensible lumped-parameter model of pile group foundation.The present method is an important extension to the concept of polynomial-fraction approximation in the foundation modeling.In the analysis,the normalized flexibility function was adopted to improve the accuracy of the model and to reduce the number of parameters in modeling.The accuracy and validity of the lumped-parameter model was extensively investigated in the case of pile group foundation.The proposed method may be easily applied to analyze various practical problems in soil-structure interaction in both frequency domain and time domain.
The pile group impedance function was considered based on thin layer method,and attention was paid on the application of Chebyshev complex polynomials in the development of extensible lumped-parameter model of pile group foundation.The present method is an important extension to the concept of polynomial-fraction approximation in the foundation modeling.In the analysis,the normalized flexibility function was adopted to improve the accuracy of the model and to reduce the number of parameters in modeling.The accuracy and validity of the lumped-parameter model was extensively investigated in the case of pile group foundation.The proposed method may be easily applied to analyze various practical problems in soil-structure interaction in both frequency domain and time domain.
引文
[1]蒋通,程昌熟.用薄层法分析高架轨道交通引发的环境振动[J].振动工程学报,2007,20(6):623-628.
[2]Wass G.Linear two-dimensional analysis of soil dynamicproblems in semi-infinite layered media[D].Univ.ofCalifornia,Berkeley,Calif.,1972.
[3]田治見宏,下村幸男.3次元薄層要素による建物ー地盤系の動的解析[C].日本建築学会論文報告集,1976,243:41-51.
[4]Tajimi H.A contribution to theoretical prediction on dynamicstiffness surface foundations[C].Proc.7WCEE,1980,5:105-112.
[5]田治見宏.埋設円形基礎の動的剛性算定のためのリング加振解の誘導[C].第9回日本地震工学シンポジウム.1994,1141-1146.
[6]Wass G,Hartmann H G.Analysis of pile foundation underdynamic loads[C].Smi RT,1981,K5/2.
[7]長谷川正幸,中井正一,福和伸夫.薄層法による2次元加振解の誘導とその応用(その1)点加振薄層解の誘導[C].日本建築学会大会学術講演梗概集,1983:785-786.
[8]長谷川正幸.弾性波動論に基ついた群杭の挙動に関する基礎的研究[R].ORI研究報告,1993.
[9]Tajimi H.Predicted and measured vibrational characteristicsof a large-scale shaking table foundation[C].Proc.8WCEE,1984,3:873-880.
[10]下村幸男,池田能夫,田治見宏.薄層地盤ばねを用いた埋め込み構造物の実用な動的解析手法[C].構造工学論文集,1991,37B:57-70.
[11]蒋通,程昌熟.用二次形函数薄层法分析弹性层状地基中的动力问题[J].力学季刊,2006,27(3):495-504.
[12]蒋通,程昌熟.用薄层法分析层状地基中各种基础的阻抗函数[J].力学季刊,2007,28(2):180-186.
[13]蒋通,田治见宏.地基-结构动力相互作用分析方法———薄层法原理及应用[M].上海:同济大学出版社,2009.
[14]严人觉,王贻荪,韩清宇.动力基础半空间理论概念[M].北京:中国建筑工业出版社,1981.
[15]Wolf J P,Somaini D R.Approximate dynamic model ofembedded foundation in time domain[J].EarthquakeEngineering and Structural Dynamics,1986,14(5),683-703.
[16]De Barros F C P,Luco J E.Discrete models for verticalvibrations of surface and embedded foundations[J].Earthquake Engineering and Structural Dynamics,1990,19(2),289-303.
[17]Takemiya H.Simplified model for building-foundationinteraction[J].Journal of the Engineering MechanicsDivision,ASCE,1976,103(2):345-351.
[18]栗茂田,林皋.地基动力阻抗的双白由度集总参数模型[J].大连理工大学学报,1996,36(4):477-481.
[19]Wolf J P.Spring-dashpot-mass models for foundationvibrations[J].Earthquake Engineering and StructuralDynamics,1997,26(9):931-949.
[20]Wu W H,Chen C Y.Simple lumped-parameter models offoundation using mass-spring-dashpot oscillators[J].Journalof the Chinese Institute of Engineers,2001,24(6):681-697.
[21]Wu W H,Lee W H.Systematic lumped-parameter models forfoundations based on polynomial-fraction approximation[J].Earthquake Engineering and Structural Dynamics,2002,31(7):1383-1412.
[22]Wu W H,Lee W H.Nested lumped-parameter models forfoundation vibrations[J].Earthquake Engineering andStructural Dynamics,2004,33(9):1051-1058.
[23]Zhou D.Three-dimensional vibration analysis of structuralelements using Chebyshev-Ritz method[M].Beijing:Science Press,2007.
[2]Wass G.Linear two-dimensional analysis of soil dynamicproblems in semi-infinite layered media[D].Univ.ofCalifornia,Berkeley,Calif.,1972.
[3]田治見宏,下村幸男.3次元薄層要素による建物ー地盤系の動的解析[C].日本建築学会論文報告集,1976,243:41-51.
[4]Tajimi H.A contribution to theoretical prediction on dynamicstiffness surface foundations[C].Proc.7WCEE,1980,5:105-112.
[5]田治見宏.埋設円形基礎の動的剛性算定のためのリング加振解の誘導[C].第9回日本地震工学シンポジウム.1994,1141-1146.
[6]Wass G,Hartmann H G.Analysis of pile foundation underdynamic loads[C].Smi RT,1981,K5/2.
[7]長谷川正幸,中井正一,福和伸夫.薄層法による2次元加振解の誘導とその応用(その1)点加振薄層解の誘導[C].日本建築学会大会学術講演梗概集,1983:785-786.
[8]長谷川正幸.弾性波動論に基ついた群杭の挙動に関する基礎的研究[R].ORI研究報告,1993.
[9]Tajimi H.Predicted and measured vibrational characteristicsof a large-scale shaking table foundation[C].Proc.8WCEE,1984,3:873-880.
[10]下村幸男,池田能夫,田治見宏.薄層地盤ばねを用いた埋め込み構造物の実用な動的解析手法[C].構造工学論文集,1991,37B:57-70.
[11]蒋通,程昌熟.用二次形函数薄层法分析弹性层状地基中的动力问题[J].力学季刊,2006,27(3):495-504.
[12]蒋通,程昌熟.用薄层法分析层状地基中各种基础的阻抗函数[J].力学季刊,2007,28(2):180-186.
[13]蒋通,田治见宏.地基-结构动力相互作用分析方法———薄层法原理及应用[M].上海:同济大学出版社,2009.
[14]严人觉,王贻荪,韩清宇.动力基础半空间理论概念[M].北京:中国建筑工业出版社,1981.
[15]Wolf J P,Somaini D R.Approximate dynamic model ofembedded foundation in time domain[J].EarthquakeEngineering and Structural Dynamics,1986,14(5),683-703.
[16]De Barros F C P,Luco J E.Discrete models for verticalvibrations of surface and embedded foundations[J].Earthquake Engineering and Structural Dynamics,1990,19(2),289-303.
[17]Takemiya H.Simplified model for building-foundationinteraction[J].Journal of the Engineering MechanicsDivision,ASCE,1976,103(2):345-351.
[18]栗茂田,林皋.地基动力阻抗的双白由度集总参数模型[J].大连理工大学学报,1996,36(4):477-481.
[19]Wolf J P.Spring-dashpot-mass models for foundationvibrations[J].Earthquake Engineering and StructuralDynamics,1997,26(9):931-949.
[20]Wu W H,Chen C Y.Simple lumped-parameter models offoundation using mass-spring-dashpot oscillators[J].Journalof the Chinese Institute of Engineers,2001,24(6):681-697.
[21]Wu W H,Lee W H.Systematic lumped-parameter models forfoundations based on polynomial-fraction approximation[J].Earthquake Engineering and Structural Dynamics,2002,31(7):1383-1412.
[22]Wu W H,Lee W H.Nested lumped-parameter models forfoundation vibrations[J].Earthquake Engineering andStructural Dynamics,2004,33(9):1051-1058.
[23]Zhou D.Three-dimensional vibration analysis of structuralelements using Chebyshev-Ritz method[M].Beijing:Science Press,2007.
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