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An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation

机译:弹性基础上功能梯度厚矩形板自由振动的有效剪切变形理论

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摘要

Free vibration analysis of plates made of functionally graded materials and resting on elastic foundation is presented by taking into account the effect of transverse shear deformations. The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The formulation is based on a higher order hyperbolic shear deformation theory. The equation of motion for thick functionally graded plates is obtained through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature.
机译:通过考虑横向剪切变形的影响,提出了功能梯度材料制成的板并置于弹性基础上的自由振动分析。基础由Pasternak(两参数)模型描述。假定板的材料特性通过简单的幂定律分布沿厚度方向在成分的体积分数方面连续变化。该公式基于高阶双曲剪切变形理论。厚功能梯度板的运动方程是根据汉密尔顿原理获得的。通过使用Navier技术获得封闭形式的解,然后通过求解特征值问题的结果来找到基频。通过将数值示例的结果与文献中提供的结果进行比较,可以显示本配方的准确性。

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