横观各向同性饱和地基与中厚圆板的非轴对称动力相互作用  

Dynamic Interaction between Elastic Thick Circular Plate and Transversely Isotropic Saturated Soil Ground

作　　者：黄义[1] 王小岗[1] 

机构地区：[1]西安建筑科技大学理学院,西安710055

出　　处：《应用数学和力学》2005年第9期1045-1054,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(59678003)

摘　　要：研究横观各向同性饱和土地基上中厚弹性圆板的非轴对称振动问题,即首先利用Fourier展开和Hankel变换技术,求解了简谐激励下横观各向同性饱和土地基的非轴对称Biot波动方程,然后按混合边值问题建立地基与弹性中厚圆板非轴对称动力相互作用的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程.文末给出了算例.数值结果表明,在一定频率范围内,地基表面的位移幅值随激振频率增加而增大,随距离的增大以振荡形式衰减变化.A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetical harmonic source. However, the assumption may not always by valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the techuique of Fourier expansion and Hankel transform, the governing different equation for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transfonned stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describes the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation is increased with the increase of the frequency of the exciting force, and decreased in vibration form with the increase of the distance.

关 键 词：BIOT波动方程 横观各向同性饱和土 中厚弹性圆板 振动 FREDHOLM积分方程 

分 类 号：O357.3[理学—流体力学]