Abstract: In this study, a flexural function is presented. Which Satisfies all the boundary conditions of the restangular plates with free edges on elastic foundation, the bending. Stability and vibration of free rectangular plate on the two-parameters elastic foundation are analyzed by the variational principle. This method is fast and simple to be used and with very high accuracy which is worthy of being extended in engineeriy In this paper, the previous results of free rectangular plate on the winker elastic foundation have also been improved.

Key words: two parameters elastic foundation, rectangular plates with free edges, flexural function, variational principle

摘要： 本文首次提出一条挠曲函数,它严格满足弹性地基上自由边矩形板的全部内力、几何边界条件然后,运用变分法对双参数弹性地基上自由边矩形板的弯曲、稳定和振动问题进行求解。此法计算过程简捷,精度高,适宜在工程计算中推广。文中还顺便改进了Winkler弹性地基上自由边矩形板的已有结果。

关键词: 双参数弹性地基, 自由边矩形板, 挠曲函数, 变分法