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Imperfection sensitivity in the nonlinear vibration of initially stresses functionally graded plates

机译：初应力功能梯度板的非线性振动中的缺陷敏感性

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In this paper, the nonlinear partial differential equations of nonlinear vibration for an imperfect functionally graded plate (FGP) in a general state of arbitrary initial stresses are presented. The derived equations include the effects of initial stresses and initial imperfections size. The material properties of a FGP are graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of the constituents. Using these derived governing equations, the nonlinear vibration of initially stressed FGPs with geometric imperfection was studied. The present approach employed a perturbation technique, the Galerkin method and the Runge-Kutta method. The perturbation technique was used to derive the nonlinear governing equations. The motion of imperfect FGPs was obtained by performing the Galerkin method and then solved by the Runge-Kutta method. Numerical solutions are presented for the performances of perfect and imperfect FGPs. The nonlinear vibration of a simply supported ceramic/metal FGP was solved. It is found that the initial stress, geometric imperfection and volume fraction index greatly change the behavior of nonlinear vibration.
机译：本文提出了在任意初始应力的一般状态下，不完全的功能梯度板（FGP）的非线性振动的非线性偏微分方程。导出的方程式包括初始应力和初始缺陷大小的影响。 FGP的材料特性沿厚度方向连续分级。在成分的体积分数方面，特性的变化遵循简单的幂律分布。使用这些导出的控制方程，研究了具有几何缺陷的初始应力FGP的非线性振动。本方法采用摄动技术，Galerkin方法和Runge-Kutta方法。摄动技术被用来推导非线性控制方程。通过执行Galerkin方法获得不完美的FGP的运动，然后通过Runge-Kutta方法求解。给出了完美和不完美FGP性能的数值解。解决了简单支撑的陶瓷/金属FGP的非线性振动。发现初始应力，几何缺陷和体积分数指数极大地改变了非线性振动的行为。

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