饱和地基上弹性圆板的动力响应

DYNAMIC RESPONSES OF ELASTIC CIRCULAR PLATE ON SATURATED GROUND

研究弹性圆板在饱和地基上的垂直振动特性，即首先应用Ｈａｎｋｅｌ变换方法求解饱和土波动方程，然后按混合边值条件建立饱和地基上圆板垂直振动的对偶积分方程，用一种简便的方法，对偶积分方程可化为易于数值计算的第二类Ｆｒｅｄｈｏｌｍ积分方程．文末的数值分析得出了板振动的一些规律性，由此表明当板的挠曲刚度Ｄ趋于无穷大且不计板的质量时，其结果和无质量刚性圆盘在饱和地基上的振动特性完全一致．

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper by the authors based on the assumption of a rigid foundation. However, the assumption of a rigid foundation may not always be valid. In this paper, the work is extended to the case of a flexible circular plate resting on saturated soil and subjected to a harmonic vertical force. The analysis is based on the theory of elastic wave in saturated soil established by the first author of this paper. By the technique of Hankel transform, the governing different equations for saturated soil are easily solved and the corresponding Hankel transformed displacement solutions are obtained. Then, under the assumption of relaxed contact conditions, i.e., frictionless contact between the plate and the surface of the saturated ground, the problem leads to a pair of dual integral equations. Next, on the combination of the equation of motion of the classic thin plate that the deflection of plate, w , must satisfy, the dual integral equations which describing the mixed boundary-value problem can be reduced to the Fredholm integral equation of the second kind and solved by numerical procedure. At the end of this paper, the compliance functions for vertical vibration of the plate bearing on saturated ground are derived, and the vertical displacement of the plate is evaluated. The numerical results show that at the limit case of D the flexural rigidity of the plate) and the mass density of the plate), the dynamic responses of a circular plate resting on the saturated soils are in exactly agreement with those of a massless rigid circular footing previously presented.