水利学报
水利學報
수리학보
2013年
7期
835-841,847
,共8页
积分型本构方程%黏弹性%水平振动%动力阻抗%黏性系数
積分型本構方程%黏彈性%水平振動%動力阻抗%黏性繫數
적분형본구방정%점탄성%수평진동%동력조항%점성계수
integral constitutive equations%viscoelasticity%lateral vibration%dynamic impedance%viscosity coefficient
基于土动力学、黏弹性理论和分数阶导数理论建立了分数阶三维积分型黏弹性土体水平振动控制方程。利用势函数对分数阶三维积分型黏弹性土体的水平振动方程进行解耦，借助分离变量法在频率内求解了分数阶三维积分型黏弹性土体的水平振动，得到了土体对单桩的水平作用，进而建立了分数阶三维积分型黏弹性土体中单桩的水平振动方程。考虑单桩的边界条件和桩顶水平动力阻抗的定义，求解了单桩的水平振动，并对桩顶水平动力阻抗进行了数值分析和讨论。研究表明：高频时，分数导数的阶数对水平动力阻抗有影响，土体黏性系数较小时水平动力阻抗实部和虚部随频率的变化曲线存在波动现象；长径比越大，水平动力阻抗越小，长径比达到一定程度时其对水平动力阻抗几乎没有影响。
基于土動力學、黏彈性理論和分數階導數理論建立瞭分數階三維積分型黏彈性土體水平振動控製方程。利用勢函數對分數階三維積分型黏彈性土體的水平振動方程進行解耦，藉助分離變量法在頻率內求解瞭分數階三維積分型黏彈性土體的水平振動，得到瞭土體對單樁的水平作用，進而建立瞭分數階三維積分型黏彈性土體中單樁的水平振動方程。攷慮單樁的邊界條件和樁頂水平動力阻抗的定義，求解瞭單樁的水平振動，併對樁頂水平動力阻抗進行瞭數值分析和討論。研究錶明：高頻時，分數導數的階數對水平動力阻抗有影響，土體黏性繫數較小時水平動力阻抗實部和虛部隨頻率的變化麯線存在波動現象；長徑比越大，水平動力阻抗越小，長徑比達到一定程度時其對水平動力阻抗幾乎沒有影響。
기우토동역학、점탄성이론화분수계도수이론건립료분수계삼유적분형점탄성토체수평진동공제방정。이용세함수대분수계삼유적분형점탄성토체적수평진동방정진행해우，차조분리변량법재빈솔내구해료분수계삼유적분형점탄성토체적수평진동，득도료토체대단장적수평작용，진이건립료분수계삼유적분형점탄성토체중단장적수평진동방정。고필단장적변계조건화장정수평동력조항적정의，구해료단장적수평진동，병대장정수평동력조항진행료수치분석화토론。연구표명：고빈시，분수도수적계수대수평동력조항유영향，토체점성계수교소시수평동력조항실부화허부수빈솔적변화곡선존재파동현상；장경비월대，수평동력조항월소，장경비체도일정정도시기대수평동력조항궤호몰유영향。
The lateral dynamic equations of viscoelastic soil described by fractional derivative three-dimen-sional integral constitutive relationship has been established based on soil dynamics, viscoelastic theory and theory of fractional derivative. The horizontal dynamic equations of the viscoelastic soil are decoupled by us-ing potential functions, the lateral vibration of the viscoelastic soil is solved and obtained the horizontal force of the soil acting on the pile with the method of separation of variables, and the horizontal dynamic equation of the single pile in the viscoelastic soil is described by fractional derivative three-dimensional in-tegral constitutive relationship. The lateral vibration of the single is solved by considering the boundary con-ditions and the definition of dynamic impedance of the pile at pile head, and the numerical analysis and discussion of the dynamic impedance of the pile is also investigated. The research indicates that the order of fractional derivative has effect on the dynamic impedance of the pile at pile head for higher frequency, and the curves of the real part and image part of lateral dynamic impedance varying with frequency have fluctuations when the soil viscosity coefficient is smaller;the larger the ratio of length to diameter, the smaller lateral dynamic impedance will be, and the ratio of length to diameter has almost no effect on the lateral dynamic impedance when it increases to a certain extent.
