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首页> 美国卫生研究院文献>Materials >Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method
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Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

机译：基于半解析法的弹性梯度地基功能梯度夹心矩形板的三维振动分析

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摘要

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.
机译：利用基于三维弹性理论的半解析法，对功能梯度夹心矩形板在弹性边界条件下的三维振动进行了分析。夹心板的材料特性根据幂律分布随厚度而变化。本文研究了两种类型的功能梯度材料（FGM）夹心板：一种具有均质的芯和FGM面板，另一种具有均质的面板和FGM芯。使用改进的傅立叶级数（包括标准傅立叶余弦级数）以及一定数量的满足基本边界条件的闭合形式辅助函数，可以创建板的各种位移。使用Ritz方法获得了FGM夹层板的振动特性，包括固有频率和振型。通过将夹心板的固有频率与文献中其他功能梯度夹心矩形板的研究结果进行比较，充分验证了所建议技术的有效性和准确性。进行了参数研究，包括弹性参数，基础参数，幂律指数和层厚比，并提出了一些新的结果。

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