弹性地基上圆底扁球壳的非线性动力问题

本文从Krmn非线性基本微分方程出发,提出了将修正迭代法和伽辽金法联合运用,分析了弹性地基上圆底扁球壳在均布荷载作用下周边固定边界条件的非线性动力响应问题,给出了中心振幅与时间t之间关系的二次近似解析表达式;同时还讨论了Winkler地基参数K对中心最大振幅的影响。此外将本文的部分结果和已有文献结果作了比较,二者吻合较好。

Non-linear Dynamic Problems of Shallow Spherical Shells on Elastic Foundations

Based on Karmane's type non-linear differential equations of shallow shells, a now approach which combines the modified iteration method with the Galerkin's method, has been put forward in this paper for solving the nonlinear dynamic problems on Winkler foudation under uniform loads and clamped immovable edge conditions. The analytic expression of second approximation for amplitude-time has been given. Influence of foundational parameter on the largest amplitude has been discussed. A portion of results has been compared with existing results, and they are quite close to each other.