上覆单相弹性层饱和地基上弹性基础的竖向振动分析

THE VERTICAL VIBRATION OF AN ELASTIC FOUNDATION ON ELASTIC SOILS WITH SATURATED SUBSTRATUM

基于Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上弹性基础竖向振动的对偶积分方程.利用正交多项式将对偶积分方程化简,得到了动力柔度系数随无量纲频率b0的变化关系曲线,从而得到了上覆单相弹性层饱和地基上弹性基础的竖向振动规律.数值分析结果表明,对于弹性基础,当弹性基础的挠曲刚度较大时,发现弹性基础的竖向振动特性与刚性基础的类同,可忽略挠曲刚度对竖向振动的影响,且当无量纲频率较小的时候,动力柔度系数Cv随着无量纲频率b0的变化而发生显著的变化,但当无量纲频率b0较大的时候,动力柔度系数Cv受无量纲频率的影响较小,甚至基本上不受影响.当弹性基础的挠曲刚度较小时,随着挠曲刚度的减小,弹性基础的竖向振动将发生显著的变化,动力柔度系数Cv的实部和虚部的绝对值均变大.

Based on the Biot＇s dynamic equations,the vertical vibration of an elastic strip foundation resting on saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of Fourier integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is established under the consideration of mixed boundary-value condition and the continuity condition. The set of dual integral integral equations are converted to linear equations by means of infinite series of orthogonal functions-the Jacobi polynomials. Consequently,the dynamic compliance Cv of an elastic foundation versus the dimensionless frequency b0 is evaluated. Numerical results indicate that： when the flexible rigidity of the elastic footing is large, the characters of the vertical vibration of the elastic strip footing is similar to that of a rigid strip footing,and the effect of the flexible rigidity can be neglected. The effect of the dimensionless frequency b0 of the dynamic complicance efficient is remarkable when the dimensionless frequency b0 is small; When the dimensionless frequency b0 is large,the effect of the dimensionless frequency b0 can be neglected. When the flexible rigidity is small,with the decrease of the flexible rigidity,the absolute value of real and imaginary part of the dynamic complicance efficient increases.