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Exact closed-form free vibration analysis for functionally graded microano plates based on modified couple stress and three-dimensional elasticity theories

机译：基于改进的耦合应力和三维弹性理论的功能梯度微/纳米板的精确闭合形式自由振动分析

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In the present manuscript, a model for static and vibration of functionally graded (FG) microano plates is developed based on modified couple stress and three-dimensional elasticity theories. This three-dimensional model contains one length scale parameter to consider the small size effect. The equations of motion and boundary conditions are derived using Hamilton's principle. Analytical closed-form solutions are presented for both in-plane and out-of-plane free vibrations of simply supported plates. To obtain the analytical solutions, elasticity modulus and mass density are assumed to vary exponentially through the plate thickness, while Poisson's ratio and length scale parameter are set to constant values. Finally, some numerical results are presented and the effects of length scale parameter and material gradient index on the natural frequencies for FG microano plates are discussed. (C) 2015 Elsevier Ltd. All rights reserved.
机译：在本手稿中，基于改进的耦合应力和三维弹性理论，开发了功能梯度（FG）微/纳米板的静态和振动模型。该三维模型包含一个长度比例参数，以考虑小尺寸效应。运动和边界条件方程是根据汉密尔顿原理导出的。针对简单支撑板的平面内和平面外自由振动，提出了解析形式的解析解。为了获得解析解，假定弹性模量和质量密度在板厚范围内呈指数变化，而泊松比和长度比例参数设置为恒定值。最后，给出了一些数值结果，并讨论了长度尺度参数和材料梯度指数对FG微/纳米板固有频率的影响。 （C）2015 Elsevier Ltd.保留所有权利。

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