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首页> 外文期刊>Acta Mechanica >3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method
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3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method

机译：二维微分求积法在帕斯捷尔纳克弹性地基上厚功能梯度环形扇形板的3D自由振动分析

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摘要

Early studies on annular sector plate vibrations were focused on two-dimensional theories, such as the classical plate theory and the first- and the higher-order shear deformation plate theories. These plate theories neglect transverse normal deformations and generally assume that a plane stress state of deformation prevails in the plate. These assumptions may be appropriate for thin plates. In this paper, free vibration of thick functionally graded annular sector plates with simply supported radial edges on a two-parameter elastic foundation, based on the three-dimensional theory of elasticity, using differential quadrature method for different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of differential quadrature method and series solution is adopted to solve the equations of motion. The material properties change continuously through the thickness of the plate, which can vary according to a power law, exponentially, or any other formulations in this direction. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future research.
机译：环形扇形板振动的早期研究集中在二维理论上，例如经典板理论以及一阶和高阶剪切变形板理论。这些板理论忽略了横向法向变形，通常假定板中存在平面应力变形状态。这些假设可能适用于薄板。本文基于二维三维弹性理论，基于微分求积法，在不同的圆形边缘条件下，包括简单支撑夹固的情况下，在二维弹性基础上，利用径向边简单支撑的厚功能梯度环形扇形板的自由振动，夹紧和自由夹紧。采用由微分求积法和级数解组成的半解析法求解运动方程。材料特性在板的厚度上连续变化，该厚度可以根据幂律或该方向上的任何其他公式根据幂定律变化。准备了板的固有频率的一些新结果，包括基础弹性系数，边界条件，材料和几何参数的影响。新结果可以用作将来研究的基准解决方案。

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