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Geometrically nonlinear free vibration of FG-GPLRC circular plate on the nonlinear elastic foundation

机译：非线性弹性基础FG-GPLRC圆形板的几何非线性自由振动

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The current article deals with the nonlinear free vibration of nanocomposite circular plates reinforced with graphene platelets (GPL). The functionally graded (FG) plate is considered over a three parameter non-linear elastic foundation. In this research, three types of gradings are assumed for reinforcing the plate by GPLs. The Halpin-Tsai micromechanical rule is exploited to obtain the elastic modulus of the plate. The first order shear deformation plate theory associated with the nonlinear strain-displacement relations are applied to extract the governing motion equations. The generalized differential quadrature (GDQ) method is implemented to solve the equations of motion in the plate domain. Furthermore, an iterative displacement control technique associated with the weighted residual technique are used to linearize the present problem and obtain the linear and nonlinear frequencies. After examining the validation study, some parametric studies are tabulated and plotted to recognize the effects of the boundary condition, distribution types of GPL, GPL weight fraction, geometrical parameters, and elastic foundation parameters on the linear and non-linear free vibration behaviour of structure. It is shown that maximum frequencies of the plate belong to the FG-X case and the minimum ones are obtained in FG-O type.
机译：本文涉及用石墨烯血小板（GPL）加强的纳米复合圆形板的非线性自由振动。在三个参数非线性弹性基础上考虑功能梯度（FG）板。在该研究中，假设三种类型的等级通过GPLS加强板。利用Halpin-TSAI微机械规则以获得板的弹性模量。应用与非线性应变位移关系相关的第一阶剪切变形板理论以提取控制运动方程。实现了广义差分正交（GDQ）方法以解决板域中的运动方程。此外，与加权残差技术相关联的迭代位移控制技术用于线性化本问题并获得线性和非线性频率。在检查验证研究后，一些参数化研究表明并绘制了识别边界条件，GPL，GPL重量分数，几何参数，几何参数和弹性基础参数对结构的线性和非线性自由振动行为的影响。结果表明，板的最大频率属于FG-X情况，并且在FG-O类型中获得最小频率。

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