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Nonlinear vibrations of laminated and sandwich rectangular plates with free edges. Part 1: Theory and numerical simulations

机译：具有自由边缘的层压和夹心矩形板的非线性振动。第1部分：理论和数值模拟

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摘要

Nonlinear vibrations of completely free laminated and sandwich rectangular plates are investigated for the first time. The equations of motion are obtained via multi-modal energy approach based on Lagrange equations and by using classical and higher-order shear deformation theories with von Karman type non-linearities. The numerical analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and modes of vibration. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with quadratic and cubic nonlinear terms is obtained. A code based on pseudo arc-length continuation and collocation scheme is used for bifurcation analysis and the near resonance nonlinear vibrations are studied. The frequency-response curves, time histories and phase space diagrams are presented.
机译：首次研究了完全自由的叠层和夹心矩形板的非线性振动。通过基于Lagrange方程的多模态能量方法，以及使用具有von Karman型非线性的经典和高阶剪切变形理论，可以得出运动方程。数值分析分两个步骤进行。首先，根据切比雪夫多项式扩展板的位移和旋转，并进行线性分析以获得固有频率和振动模式。然后，利用振动的自然模式离散化能量函数，并获得了具有二次和三次非线性项的非线性常微分方程组。使用基于伪弧长连续和搭配方案的代码进行分叉分析，并研究了近共振非线性振动。给出了频率响应曲线，时间历史和相空间图。

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  • 来源
    《Composite Structures》 |2013年第11期|422-436|共15页
  • 作者

    Farbod Alijani; Marco Amabili;

  • 作者单位

    Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal H3A 0C3, Canada;

    Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal H3A 0C3, Canada;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Nonlinear vibrations; Laminated plate; Sandwich plate; Free edges;

    机译：非线性振动;层压板夹心板;自由边缘;

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