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Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

机译:FGPM环形板剪切致弯曲振动的自由振动的广义差分求积法

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This work deals with free vibration analysis of functionally graded piezoelectric (FGPM) annular plate excited using the shear effect. The shear piezoelectric coupling coefficient is higher than other piezoelectric coupling coefficients for longitudinal and lateral deformation. This makes it more attractive for engineering applications. A modified Mindlin plate theory is employed where the electric potential is assumed to have a sinusoidal variation through the thickness direction. Material constants are assumed to have a power law variation across the thickness. Theoretical formulations are derived by using Hamilton's principle. The available equations of motion are then solved using the Generalized Differential Quadrature (GDQ) method to obtain the natural frequencies of the FGPM annular plate. The accuracy of the method is validated by comparing the results with the previous study for the reduced case of isotropic plate. As there are no published work to validate the results therefore the results obtain by finite element modeling using COMSOL (version 4.2) software are used for validation. It is found that results obtained by proposed formulation are in good agreement with the results obtained by COMSOL software. The effect of plate thickness, volume fraction indices, diameter ratio and boundary conditions on natural frequencies are also reported. (C) 2016 Elsevier Ltd. All rights reserved.
机译:这项工作涉及利用剪切效应激发的功能梯度压电(FGPM)环形板的自由振动分析。对于纵向和横向变形,剪切压电耦合系数高于其他压电耦合系数。这使其对工程应用更具吸引力。采用修改的Mindlin板理论,其中假定电势在厚度方向上具有正弦变化。假设材料常数在整个厚度上具有幂律变化。理论公式是根据汉密尔顿原理得出的。然后使用广义差分正交(GDQ)方法求解可用的运动方程,以获得FGPM环形板的固有频率。通过将结果与先前研究的各向同性板的减小情况进行比较,验证了该方法的准确性。由于没有公开的工作来验证结果,因此使用COMSOL(4.2版)软件通过有限元建模获得的结果用于验证。发现通过建议的配方获得的结果与通过COMSOL软件获得的结果非常吻合。还报告了板厚度,体积分数指数,直径比和边界条件对固有频率的影响。 (C)2016 Elsevier Ltd.保留所有权利。

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