分数导数粘弹性土层中单桩扭转振动的研究

Torsional vibration of single pile in soil described by fractional derivative viscoelastic model

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.