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Numerical solution for free vibration frequency of stiffened skew plate on elastic foundation

DOI：

 作者 单位 E-mail 吴宇 广西大学土木建筑工程学院 395937471@qq.com 吴天文 广西大学 覃霞 广西大学 彭林欣 广西大学 penglx@gxu.edu.cn

为了实际地基工程中的经济效益和提供技术指标参考，本文应用无网格法计算加肋斜板在地基上的自由振动行为，应用移动最小二乘近似和一阶剪切变形原理描述加肋斜板的位移场，分别建立斜板与肋条的势能泛函，使用Winkler弹性地基模型处理加肋板与地基之间的接触势能。通过斜板与肋条的位移协调关系寻找斜板和肋条节点参数转换公式，确立加肋斜板的自由振动控制方程。本文运用了无网格法的优势，即使肋条位置改变也不需重置网格。通过本文解和有限元解作算例对比，验证本文方法的有效性和精确性。

Meshfree method was used to calculate the free vibration behaviors of a ribbed skew plate on foundation for the economic and technology index of practical foundation engineering. Displacement field of the skew plate was depicted by the moving-least square approximation and the first-order shear deformation theory, and then potential energy functional was established. The contact potential energy between the ribbed plate and foundation was simulated by Winkler elastic foundation module. The nodal parameter transformation equation was established according to the displacement compatible condition between the plate and ribs, and the governing equation for free vibration of stiffened skew plate on elastic foundation was founded. Position change of ribs would not reset the meshes because of the advantages of the proposed method, and the cost of calculation was reduced. The proposed method was verified by comparing results with those from the finite element method.
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