悬臂式蜂窝夹层板的非线性动力学建模及分析

蜂窝夹层结构因其良好的力学特性,在众多工程领域具有非常广泛的应用.本文建立了悬臂边界条件下,蜂窝夹层板的动力学模型并研究其非线性动力学行为.选取文献中更加接近实体有限元解的等效弹性参数公式对蜂窝芯层进行等效简化,得到六角形蜂窝芯的等效弹性参数.基于Reddy高阶剪切变形理论,应用Hamilton原理建立悬臂式蜂窝夹层板在受到面内激励和横向激励联合作用下的偏微分运动方程.然后利用Galerkin方法得到两自由度非自治常微分形式运动方程.在此基础上,通过对悬臂式蜂窝夹层板进行数值模拟分析系统的非线性动力学.结果表明面内激励和横向激励对系统的动力学特性有着重要影响,在不同激励作用下系统会出现周期运动、概周期运动以及混沌运动等复杂的非线性动力学响应.

Nonlinear dynamic modeling and analysis for a cantilever honeycomb sandwich plate

Honeycomb sandwich structures have been widely used in many engineering fields because of their excellent mechanical properties. The formulas for the cantilever honeycomb sandwich plate are derived, and the nonlinear vibrations of the plate are given in this paper. In order to obtain the equivalent elastic parameters of the hexagonal core layer in the honeycomb sandwich plate, the equivalent elastic parameters that more closer to the finite element solutions for the cores are selected. Based on the Reddy's third-order shear deformation theory, the nonlinear partial differential equations of motion are derived for the composite laminated cantilever plate subjected to in-plane and transverse excitations by using the Hamilton's principle. The Galerkin method is then used to transform the nonlinear partial differential equations of motion to a two-degree-of-freedom nonlinear system ordinary differential equation of motion. The numerical method is also utilized to examine the nonlinear dynamic respon ses of the cantilever honeycomb sandwich plate. The results show that in-plane and transverse excitations have an important influence on nonlinear dynamic characteristics, and periodic, multi-periodic, quasi-periodic motions and chaotic motions all occur for the system with the change of forcing loads.