分数导数粘弹性土层中单桩扭转振动的研究
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摘要
在忽略土体径向位移和竖向位移的情况下,利用分数导数粘弹性模型描述土体的应力和应变关系,建立了分数导数粘弹性土层的扭转振动控制方程,并借助于贝赛尔方程和桩端边界条件求解了分数导数粘弹性土层的扭转振动的解。考虑到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扭转振动的解,并分析了主要桩土参数对分数导数粘弹性土层中单桩扭转复刚度的影响。研究表明:分数导数的阶数对桩顶复刚度的影响很小,而土体的本构模型参数、桩土模量比和桩的长径比对桩顶复刚度的影响较大。
Under the condition of neglecting the radial and vertical displacement of the soil,the torsional vibration control equations of the soil were established,in which the relationship of stress and strain was described by fractional derivative visco-elastic model,and the torsional vibration of fractional derivative visco-elastic soil layer was solved by employing the Bessel equation and considering boundary conditions of the pile.The solution of the torsional vibration of the pile in soil described by fractional derivative visco-elastic model was obtained by considering the continuous conditions at the soil-pile and the orthogonality of trigonometric functions,and the influence of the main parameters of pile and soil on the torisonal complex stiffness was analyzed.The results indicate that the order of fractional derivative had little effect on torsional complex stiffness,and the model parameters of soil,modulus ratio and length-diameter ratio had great effects on the torsional complex stiffness.
Under the condition of neglecting the radial and vertical displacement of the soil,the torsional vibration control equations of the soil were established,in which the relationship of stress and strain was described by fractional derivative visco-elastic model,and the torsional vibration of fractional derivative visco-elastic soil layer was solved by employing the Bessel equation and considering boundary conditions of the pile.The solution of the torsional vibration of the pile in soil described by fractional derivative visco-elastic model was obtained by considering the continuous conditions at the soil-pile and the orthogonality of trigonometric functions,and the influence of the main parameters of pile and soil on the torisonal complex stiffness was analyzed.The results indicate that the order of fractional derivative had little effect on torsional complex stiffness,and the model parameters of soil,modulus ratio and length-diameter ratio had great effects on the torsional complex stiffness.
引文
[1]刘东甲,刘煜洲,王杰英.扭转波应用与低应变动力测桩的理论研究[J].岩土工程学报,2003,25(3):283-287.
[2]胡昌斌,张涛.桩土耦合扭转振动理论研究与特性分析[J].岩土工程学报,2007,29(2):184-190.
[3]王国才,王哲,陈龙珠,等.均匀弹性地基中单桩的扭转振动特性研究[J].岩土力学,2008,29(11):3027-3036.
[4]胡昌斌,张涛.基于平面应变简化假定的桩扭转振动理论精度研究[J].地震工程与工程振动,2008,28(3):122-130.
[5]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[6]Bagley R L,Torvik PJ.Atheoretical basis for the applicationof fractional calculus to viscoelasticity[J].Journal of Rheolo-gy,1983.27(3):201-210.
[7]Ti moshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book,1934.
[8]Drozdov A,Kalamkarov A L.Constitutive model for nonlin-ear viscoelastic behavior of polymer[J].Polymer Engrg.&Sci.,1996,36(14):1907-1919.
[9]Miller KS,Ross B.Anintroduction to the fractional calculusand fractional differential equations[M].New York:Wiley,1993.
[10]Nogami T,Novak M.Soil-pile interaction in vertical vibra-tion[J].Earth Engng.Stuct.Dyn.,1976,4:277-293.
[2]胡昌斌,张涛.桩土耦合扭转振动理论研究与特性分析[J].岩土工程学报,2007,29(2):184-190.
[3]王国才,王哲,陈龙珠,等.均匀弹性地基中单桩的扭转振动特性研究[J].岩土力学,2008,29(11):3027-3036.
[4]胡昌斌,张涛.基于平面应变简化假定的桩扭转振动理论精度研究[J].地震工程与工程振动,2008,28(3):122-130.
[5]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[6]Bagley R L,Torvik PJ.Atheoretical basis for the applicationof fractional calculus to viscoelasticity[J].Journal of Rheolo-gy,1983.27(3):201-210.
[7]Ti moshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book,1934.
[8]Drozdov A,Kalamkarov A L.Constitutive model for nonlin-ear viscoelastic behavior of polymer[J].Polymer Engrg.&Sci.,1996,36(14):1907-1919.
[9]Miller KS,Ross B.Anintroduction to the fractional calculusand fractional differential equations[M].New York:Wiley,1993.
[10]Nogami T,Novak M.Soil-pile interaction in vertical vibra-tion[J].Earth Engng.Stuct.Dyn.,1976,4:277-293.
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