The free vibration of a deploying laminated beam with spinning motion in hygrothermal environment is studied. The model of this system is given within the framework of the Rayleigh beam theory and the von Karman nonlinear strain theory. The nonlinear dynamic equilibrium equation of the cantilever boundary condition is established based on Hamilton's principle with considering the combined effects of the axial motion, transverse vibration, spinning motion, and hygrothermal environment. The frequencies of the system are numerically determined by using the Newmark method. The detailed parameter analyses are provided to investigate the effects of the deploying speed, the spinning speed, the temperature variation, the moisture concentration, and the fiber direction angle on frequency and the corresponding sensitivity.

中文翻译：

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湿热环境中旋转运动的展开层状瑞利梁的非线性振动

研究了湿热环境下自旋展开层合梁的自由振动问题。该系统的模型是在瑞利梁理论和冯卡门非线性应变理论的框架内给出的。基于Hamilton原理，考虑轴向运动、横向振动、自旋运动和湿热环境的综合影响，建立了悬臂边界条件的非线性动力平衡方程。系统的频率是通过使用 Newmark 方法在数值上确定的。提供了详细的参数分析，以研究展开速度、纺丝速度、温度变化、水分浓度和纤维方向角对频率和相应灵敏度的影响。