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Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method

机译：最小二乘微分求积法分析FGM板的动力稳定性

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摘要

The present paper investigates the dynamic stability of thick functionally graded material plates subjected to aero-thermomechanical loads, using a novel numerical solution technique, the moving least squares differential quadrature method. Temperature field is assumed to be a uniform distribution over the plate plane, and varied in the thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction in the simple power law manner. The equilibrium equations governing the dynamic stability of the plate are derived by the Hamilton's principle, then these equations are discretized by the moving least squares differential quadrature method. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency to load amplitude plane. The influence of various factors such as gradient index, temperature, mechanical and aerodynamic loads, thickness and aspect ratios, as well as the boundary conditions on the dynamic instability region are carefully studied.
机译：本文使用一种新型的数值求解技术，即移动最小二乘微分正交方法，研究了承受空气热机载荷的功能梯度材料厚板的动力稳定性。假定温度场在板平面上是均匀分布的，并且仅在厚度方向上变化。假定材料特性与温度有关，并以简单的幂律方式在厚度方向上分级。根据汉密尔顿原理导出了控制板动力稳定性的平衡方程，然后通过移动最小二乘微分求积法将这些方程离散化。不稳定区域的边界是使用Bolotin方法的原理获得的，并且可以方便地以无量纲激励频率表示到载荷振幅平面。仔细研究了诸如梯度指数，温度，机械和空气动力载荷，厚度和长宽比以及边界条件等因素对动态不稳定区域的影响。

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