摘要
基于作者提出的饱和土弹性波动方程，研究了饱和地基上含刚核弹性圆板在竖向集中谐 和力作用下的振动特性．首先应用Ｈａｎｋｅｌ积分变换求解该饱和土波动方程，然后按混合边值 条件建立起一组描述含刚核弹性圆板振动的对偶积分方程，并将其化为第二类Ｆｒｅｄｈｏｌｍ积分 方程进行数值求解．文末给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率 ａ０的变化曲线，并考察了土的渗透系数，弹性板含刚域的大小以及板的柔度等参数对阻抗函 数的影响，得出了一些有意义的结论．
A study of the vertical vibration of a flexible plate with rigid core resting on saturated ground is presented in this paper. The analysis is based on the theory of elastic wave in saturated soil established by the second author of the paper. We start with a derivation of the governing different equations for saturated soil by the use of Hankel transform 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 and keeping in mind that the vertical displacement of the internal rigid core of plate be a constant while the outer flexible plate must satisfy the equation of motion of the classic thin plate, an dual integral equations which describe the mixed boundary-value problem for the flexible plate with a rigid core are established which are reduced to the second kind Fredholm integral equation and solved by standard procedure. At the end of this paper, the dynamic impedance functions for vertical vibration of the plate bearing on saturated ground are derived, the effects of the permeability, the size of the rigid core and the flexibility of the plate on the impedance functions are studied. The numerical results show that at the limit case of = 0 ( = the dimensionless flexural compliance of the plate) or rb→0 (rb corresponds to the size of rigid core), the dynamic impedance functions are in exactly agreement with those for rigid plate and fully flexible plate respectively.
出处
《力学学报》
EI
CSCD
北大核心
2002年第1期77-86,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(59579018)~~
