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Analytical solutions for vibrations of laminated and sandwich plates using mixed theory

机译：混合理论对夹层板和夹层板振动的解析解

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摘要

A semi-analytical method has been presented in this paper to evaluate the natural frequencies as well as displacement and stress eigenvectors for simply supported, cross-ply laminated and sandwich plates by using higher order mixed theory. Models based on equivalent single layer as well as layerwise (LW) theories have been formulated. By assuming a non-linear variation of axial displacements through the plate thickness, the warping of the transverse cross-section has been considered. Hamilton's principle has been employed to derive the equilibrium equations. The proposed LW model fulfills a priori the continuity of displacements as well as the transverse and the normal stress components at each interface between two adjacent layers. Results obtained by present higher order mixed theory have been found in good agreement with those obtained by three-dimensional elasticity solutions. After establishing the accuracy of present results for orthotropic plates, new results for thin and thick sandwich plates have been presented which can serve as benchmark solutions for future investigations.
机译：本文提出了一种半解析方法，通过使用高阶混合理论来评估简单支撑，交叉叠层和夹层板的固有频率以及位移和应力本征向量。已经建立了基于等效单层以及逐层（LW）理论的模型。通过假设整个板厚度的轴向位移呈非线性变化，已考虑了横截面的翘曲。汉密尔顿原理已被用来推导平衡方程。所提出的LW模型先验地满足了位移的连续性以及两个相邻层之间每个界面处的横向和法向应力分量。已经发现通过当前的高阶混合理论获得的结果与通过三维弹性解获得的结果非常吻合。在确定了正交异性板当前结果的准确性之后，提出了薄板和厚夹心板的新结果，它们可以作为未来研究的基准解决方案。

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