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A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness

机译：变厚度剪切变形多边形板自由振动分析的变分方法

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摘要

This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates.rnThe governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.
机译：本文提出了一种简单通用的变分方法来研究厚度可变的多边形各向同性板的自由振动行为。使用Reissner-Mindlin板理论在分析中考虑了剪切变形和旋转惯性的影响。而且，即使对于薄板，该理论也允许获得与振动更高模式相对应的频率系数的更高精度。使用Ritz方法获得控制特征值方程。通过使用非正交三角坐标来近似板的几何形状，同时使用以这些坐标表示的独立多项式组来近似位移和旋转场。所开发的算法可以为具有不同长宽比，厚度变化和边界条件（包括通过平移和旋转弹簧弹性约束的边缘）的板材获得近似的解析解。因此，易于执行统一程序。进行了收敛和比较分析，以验证数值解的可靠性和准确性。最后，进行参数研究，并以图形和表格形式给出结果。

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