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工程力学  2014 

弹性地基上矩形薄板自由振动的精确解

DOI: 10.6052/j.issn.1000-4750.2012.12.0962, PP. 43-48

Keywords: 弹性地基,矩形薄板,自由振动,分离变量,精确解

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Abstract:

根据分离变量法得到了Winkler弹性地基上矩形薄板自由振动问题的精确解,分析了地基模量对频率的影响,其中边界条件为CCCC、SCCC和SSCC情况的精确解过去被认为是难以得到的。在分离变量方法中,不需要事先人为的选取满足某一组对边边界条件的挠度函数,而是直接利用控制方程本征根给出振型函数通解的一般解析形式,再利用边界条件得到振型函数系数和频率方程的精确形式。数值结果与有限元结果及文献结果吻合较好,验证了该文方法和结果的的正确性。

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