基于经典叠层板理论和几何大变形理论, 研究了四边固支Al质蜂窝夹芯板的非线性动力学问题. 在考虑横向阻尼的影响下, 利用Hamilton变分原理建立了蜂窝夹芯板受横向激振力作用时的受迫振动微分方程, 通过振型正交化将 蜂窝夹芯板的受迫振动微分方程简化为双模态下的动力学控制方程, 同时利用Runge-Kutta法数值模拟了系统的非线性动力学行为. 结果表明: 由于芯层六角形胞元结构的影响, 使得蜂窝夹芯板的振动对横向激振力幅值的变化非常敏感; 第一阶模态下的最大振幅总要大于第二阶模态下的最大振幅, 横向激振力幅值在不同的取值范围时, 蜂窝夹芯板存在不同性质的动力学现象, 在横向激振力幅值较小阶段, 系统总是呈现单倍周期运动. 当横向激振力幅值增加到一定数值时, 系统呈现出从周期运动向倍周期及混沌等复杂运动形式的转换.通过相应的弯曲振动响应实验, 对数值分析结果进行了实验验证.
Study on the dynamics of aluminum honeycomb sandwich plates of composite structure material plays a key role for the special applications of the aerospace and automotive engineering. The nonlinear dynamics of honeycomb sandwich plate is explored. According to the classical plate theory and the large deformation, the governing equations of motion are established for the honeycomb sandwich plate subjected to the transversal excitation force by using the Hamilton’s law of variation principle. The transversal damping is taken into consideration. The method of normalization is utilized to transform the nonlinear vibration equations to nonlinear system with double modes of freedom. Numerical simulation is used directly to investigate the nonlinear responses of the honeycomb sandwich plate. The results indicates that the change of transversal excitation force has a significant effect on the vibration of honeycomb sandwich plate because the hexagon cell of core and the amplitude of the first modal are bigger than the second modal. In the different ranges of transversal excitation force, the honeycomb sandwich plate exists different dynamical phenomena. Single periodic motion appears when the force value is small, and periodic motion, multi–period motion, chaotic motion appears with the increase of force. Experiments are conducted to validate the numerical simulation results.
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