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Winkler/Pasternak/Kerr地基上多孔FG板基于四变量板理论的自由振动分析
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Abstract:
本文提出了一种新的广义四变量板理论，用于弹性地基上孔隙依赖功能梯度材料板(porous func-tionally gradedplate，简称孔隙依赖FG板)自由振动分析。考虑了三种不同的孔隙率分布(包括均匀分布、非均匀分布和对数非均匀分布)并对三种不同的地基(Winkler-Pasternak地基和Kerr地基)行了研究。通过哈密顿原理得到控制方程，通过解特征值问题得到了数值结果，研究了不同孔隙率、长细比、幂律指数和弹性刚度参数对多孔FG板基频的影响，并将所得的结果与已有文献进行对比，验证了本文理论的准确性。
The free vibration responses of porous functionally graded plate(FG)rectangular plates resting on elastic foundations are investigated according to a novel four-variable refined plate theory. Three types of porosities distributions (even and uneven, and the logarithmic-uneven distribution) are learned. The elastic foundations are considered as Winkler-PasternakandKerr foundation. Governing equations are derived by using Hamilton principle. The effect of porosity parameter, slenderness ratio, the power-law index and parameters of elastic foundation are also investigated. The the-oretical calculation results of fundamental frequency of porous FG plates resting on elastic foundations are predicted by solving the eigenvalue problems and compared with the available results in the literature to verify the theory.
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