分数导数模型描述的粘弹性土层中桩基水平振动研究
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摘要
借助分数导数理论、粘弹性理论和土动力学理论建立了三维轴对称条件下分数导数粘弹性土层的水平振动控制方程,采用势函数和分离变量法求解了分数导数粘弹性土层的水平振动,得到了土层的水平动力阻抗。并借助于桩-土界面的连续条件和三角函数的正交性得到了分数导数粘弹性土层中单桩的水平动力阻抗。通过数值算例研究了桩土参数对分数导数粘弹性土层水平动力阻抗因子和土层中单桩水平动力阻抗的影响。研究表明:分数导数粘弹性土层的水平动力阻抗因子和分数导数粘弹性土层中桩顶水平动力阻抗可以退化为经典粘弹性和弹性土层的情况;桩土模量比对分数导数粘弹性土层中桩顶水平动力阻抗的影响与弹性情况存在较大差异。
The axisymmetric lateral vibration equations of the soil described by fractional derivative viscoelastic model are established by the theory of fractional derivative as well as viscoelastic and soil dynamics,and the lateral vibration of the soil described by a fractional derivative viscoelastic model is analyzed and obtained the lateral resistance of the soil by potential functions and separation of variables.The horizontal vibration equations of a single pile in soil are established,and the lateral dynamic impedance of the pile is obtained by considering the continuous conditions at the soil-pile and the orthogonality of trigonometric functions.The lateral resistance factor of the soil described by a fractional derivative viscoelastic model and the horizontal dynamic impedance of a single pile in soil are investigated with the numerical examples.The result indicated that the lateral resistance factor of the soil and the horizontal dynamic impedance of a single pile in soil described by a fractional derivative viscoelastic model can reduced to the cases of classic viscoelasticity and elasticity,the influence of the modulus ratio on the lateral dynamic impedance of the pile has great difference between fractional derivative viscoelastic and elastic soil.
The axisymmetric lateral vibration equations of the soil described by fractional derivative viscoelastic model are established by the theory of fractional derivative as well as viscoelastic and soil dynamics,and the lateral vibration of the soil described by a fractional derivative viscoelastic model is analyzed and obtained the lateral resistance of the soil by potential functions and separation of variables.The horizontal vibration equations of a single pile in soil are established,and the lateral dynamic impedance of the pile is obtained by considering the continuous conditions at the soil-pile and the orthogonality of trigonometric functions.The lateral resistance factor of the soil described by a fractional derivative viscoelastic model and the horizontal dynamic impedance of a single pile in soil are investigated with the numerical examples.The result indicated that the lateral resistance factor of the soil and the horizontal dynamic impedance of a single pile in soil described by a fractional derivative viscoelastic model can reduced to the cases of classic viscoelasticity and elasticity,the influence of the modulus ratio on the lateral dynamic impedance of the pile has great difference between fractional derivative viscoelastic and elastic soil.
引文
[1]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277―293.
[2]Novak M,Nogami T,Aboul-Ella F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics,1978,104(4):953―959.
[3]Nogami T,Konagai K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,112(11):1241―1252.
[4]Mamoon S M,Kaynia A M,Banerjee P K.Frequency-domain dynamic analysis of piles and pile groups[J].Journal of Engineering Mechanics,1990,116(10):2237―2257.
[5]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11:574―598.
[6]胡昌斌,黄晓明.成层粘弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205―211.Hu Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[7]周绪红,蒋建国,邹银生.粘弹性介质中考虑轴力作用时桩的动力分析[J].土木工程学报,2005,38(2):87―91.Zhou Xuhong,Jiang Jianguo,Zou Yinsheng.Dynamic analysis of piles under axial loading and lateral dynamic force in visco-elastic medium[J].China Civil Engineering Journal,2005,38(2):87―91.(in Chinese)
[8]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变性分析[J].工程力学,2009,26(1):13―17.Liu Linchao,Yang Xiao.Analysis on settlement of semi-infinite viscoelastic ground based on fractional derivative model[J].Engineering Mechanics,2009,26(1):13―17.(in Chinese)
[9]陈立群,程昌钧.分数导数型本构关系描述粘弹性梁的振动分析[J].力学季刊,2001,22(4):512―516.Chen Liqun,Cheng Changjun.Vibration analysis of viscoelastic beams with fractional derivative constitute relation[J].Chinese Quarterly of Mechanics,2001,22(4):512―516.(in Chinese)
[10]孙海忠,张卫.一种分析软土黏弹性的分数导数开尔文模型[J].岩土力学,2007,28(9):1983―1986.Sun Haizhong,Zhang Wei.Analysis of soft soil with viscoelastic fractional derivative Kelvin model[J].Rock and Soil Mechanics,2007,28(9):1983―1986.(in Chinese)
[11]Bagley R L,Torvik P J.A theoretical basis for the application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201―210.
[12]Timoshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book,1934.
[13]Drozdov A,Kalamkarov A L.A constitutive model for nonlinear viscoelastic behavior of polymer[J].Polymer Engineering and Science,1996,36(14):1907―1919.
[14]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley,1993.
[2]Novak M,Nogami T,Aboul-Ella F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics,1978,104(4):953―959.
[3]Nogami T,Konagai K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,112(11):1241―1252.
[4]Mamoon S M,Kaynia A M,Banerjee P K.Frequency-domain dynamic analysis of piles and pile groups[J].Journal of Engineering Mechanics,1990,116(10):2237―2257.
[5]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11:574―598.
[6]胡昌斌,黄晓明.成层粘弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205―211.Hu Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[7]周绪红,蒋建国,邹银生.粘弹性介质中考虑轴力作用时桩的动力分析[J].土木工程学报,2005,38(2):87―91.Zhou Xuhong,Jiang Jianguo,Zou Yinsheng.Dynamic analysis of piles under axial loading and lateral dynamic force in visco-elastic medium[J].China Civil Engineering Journal,2005,38(2):87―91.(in Chinese)
[8]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变性分析[J].工程力学,2009,26(1):13―17.Liu Linchao,Yang Xiao.Analysis on settlement of semi-infinite viscoelastic ground based on fractional derivative model[J].Engineering Mechanics,2009,26(1):13―17.(in Chinese)
[9]陈立群,程昌钧.分数导数型本构关系描述粘弹性梁的振动分析[J].力学季刊,2001,22(4):512―516.Chen Liqun,Cheng Changjun.Vibration analysis of viscoelastic beams with fractional derivative constitute relation[J].Chinese Quarterly of Mechanics,2001,22(4):512―516.(in Chinese)
[10]孙海忠,张卫.一种分析软土黏弹性的分数导数开尔文模型[J].岩土力学,2007,28(9):1983―1986.Sun Haizhong,Zhang Wei.Analysis of soft soil with viscoelastic fractional derivative Kelvin model[J].Rock and Soil Mechanics,2007,28(9):1983―1986.(in Chinese)
[11]Bagley R L,Torvik P J.A theoretical basis for the application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201―210.
[12]Timoshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book,1934.
[13]Drozdov A,Kalamkarov A L.A constitutive model for nonlinear viscoelastic behavior of polymer[J].Polymer Engineering and Science,1996,36(14):1907―1919.
[14]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley,1993.
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