双参数弹性地基板的动力问题

The dynamic problem of plates on the bi-parameter elastic foundations

针对目前带自由边的双参数弹性地基板的边界条件及基本方程在使用上的混乱情况,为了板与地基动力相互作用理论的严密性和计算的可靠性,将板和地基作为一个总系统,利用H am ilton动力变分原理,重新系统地审视了双参数弹性地基上板动力问题的基本理论,给出了地基附加质量影响的明确计算公式,建立了考虑地基附加质量影响的基本方程和边界条件,并对边界条件的简化进行了讨论.所得的结果还可推广到位于层状地基上的板的分析.

At present, the boundary conditions and basic equation of plates with free edges and on the bi-pararneter elastic foundations are in confusion. In this paper, plates and foundations are discussed as a total system, and the basic theory of dynamic problem about plates on the two-parameter elastic foundations are re-examlned by Hamilton＇s variation principle. The explicit expression of the additional mass of the foundations on the plates is obtained. The basic equation and boundary conditions including the additional mass of the foundations are given. At the end of paper, the simplifications for the boundary conditions of plates are discussed. The results can be extended to the analysis of plates on the layered foundations.