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Parametric stability and complex dynamical behavior of functionally graded rectangular thin plates subjected to in-plane inertial disturbance

机译：平面内惯性扰动下功能梯度矩形薄板的参数稳定性和复杂动力学行为

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摘要

In this study, the impact of in-plane inertial disturbance from environment on the dynamical behavior of a functionally graded (FG) rectangular plate is discussed. The inertial disturbance is modeled as a parametric excitation. The dynamical model of FG plate subjected to an uniaxial inertia force of an in-plane disturbance are developed according to von Karman's large deflection theory. A reduced low-dimensional nonlinear ordinary differential equations of considered FG plate are then obtained by employing Galerkin's procedure. Both multiple scales method and Floquet's theory are applied to analyze the parametric instability regions for small-deflection vibration of FG plate. The effects of nonlinearity are also discussed through numerical integration. It is found that the instability regions vary greatly with the variation of frequency ratio and it cannot come to a clear rule or regular pattern, but three regions, i.e. two principle instability areas and a combination instability area, always exist. The damping affects the parametric stability in a very complicated way. And the nonlinear nonzero response for combination resonance displays complex dynamical behaviors induced by bifurcations.
机译：在这项研究中，讨论了环境中的平面惯性扰动对功能梯度（FG）矩形板动力学行为的影响。惯性扰动被建模为参数激励。根据冯·卡曼的大挠度理论，建立了平面内扰动的单轴惯性力作用下的FG板动力学模型。然后，通过采用Galerkin程序，获得了所考虑的FG板的降维低维非线性常微分方程。运用多尺度法和Floquet理论对FG板小挠度振动的参数失稳区域进行了分析。还通过数值积分讨论了非线性的影响。已经发现，不稳定性区域随频率比的变化而变化很大，并且不能形成清晰的规则或规则模式，但是始终存在三个区域，即两个主要不稳定性区域和组合不稳定性区域。阻尼以非常复杂的方式影响参数稳定性。组合共振的非线性非零响应显示了分叉引起的复杂动力学行为。

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