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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.
Based on classical laminate theory and large deformation theory, the nonlinear dynamics of Al solid honeycomb sandwich panels with four edges are studied. Under the influence of transverse damping, Hamilton sandwich principle is used to establish the honeycomb sandwich panel The forced vibration differential equation of the transverse vibration force is simplified. The vibrational differential equation of honeycomb sandwich panel is simplified to the dynamic governing equation under the bimodal mode by the mode orthogonalization. At the same time, the Runge-Kutta method numerical simulation The results show that the vibration of honeycomb sandwich panel is very sensitive to the amplitude of lateral excitation force due to the hexagonal cell structure of the core layer. The maximum Amplitude is always greater than the maximum amplitude of the second order mode, the amplitude of the lateral excitation force in different values, the honeycomb sandwich panel there are different dynamics of the nature of the amplitude in the horizontal excitation amplitude smaller stage , The system always exhibits single period periodic motion.When the magnitude of lateral exciting force increases to a certain value, the system presents the transition from periodic motion to double period and chaos and other complex forms of motion.According to the corresponding bending vibration response The experimental results of numerical analysis were verified.