四边固支蜂窝夹层板1:3内共振非线性动力学分析

基于经典叠层板理沦和几何大变形理沦,将铝基蜂窝芯层等效为一正交异性层,等效弹性参数由修正后的Gibson公式得出,对四边固支蜂窝夹层板非线性动力学特性进行了分析.考虑横向阻尼的影响,建立了四边固支蜂窝夹层板受横向激振力作用的受迫振动微分方程,通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程,利用同伦分析方法对双模态下蜂窝夹层板的动力学控制方程进行研究,得到了1∶3内共振下的幅频特性曲线,研究了不同结构尺寸对动力学特性的影响以及蜂窝夹层板作稳态运动时的稳定性问题.论文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考.

ANALYTIC STUDY ON 1:3 INTERNAL RESONANCE NONLINEAR DYNAMICS OF HONEYCOMB SANDWICH PANELS WITH COMPLETED CLAMPED SUPPORTED BOUNDARIES

The honeycomb core of cells was modeled as a layer of orthotropic material whose physical and the mechanical properties were determined by using the corrected Gibson’s formula．According to the classical plate theory and the large deformation, the governing equations of motion are established for the honeycomb sandwich panels subjected to the transversal excitation force by using the Hamilton’s principle. The transversal damping is taken into consideration. The method of normalization is utilized to transform the nonlinear vibration equations for the honeycomb sandwich panels to nonlinear system with double modes of freedom. Using the homotopy analysis method (HAM) solves the nonlinear vibration equations of the honeycomb sandwich panels and analyzes the change of amplitude with excitation frequency and vibration parameters. The case of the 1:3 internal resonance are considered. In addition, motion stability analysis of honeycomb sandwich panels is studied in this thesis. The result of the study offers the theoretical foundation and the numerical reference for the design and the practical application of Honeycomb Sandwich.