Abstract This paper focuses on nonlinear parametric resonance behaviors of rotating composite laminated cylindrical shells subjected to periodic axial loads and hygrothermal environment. With effects of the time-varying axial loads, hygrothermal expansion deformation, Coriolis and centrifugal forces as well as the rotation-induced initial hoop tension taken into account, the nonlinear dynamic equations of the shell are obtained on the base of Love’s nonlinear shell theory and Hamilton’s principle. Then, an analytical formulation on the steady state response of the shell is derived by the method of multiple scales, and the stability conditions of trivial and nontrivial solutions are determined by the Routh–Hurwitz criterion. Some numerical results are utilized to conduct detailed parametric studies on vibration characteristics, amplitude–frequency response curves and instability regions of forward and backward travelling waves of the shell. Of particular interest in the process is the combined effect of dynamic axial loads and hygrothermal effects on the resonance behaviors of the rotating nonlinear cylindrical shell.

中文翻译：

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周期性轴向载荷和湿热环境下旋转复合层压非线性圆柱壳的参数共振

摘要 本文重点研究了旋转复合层合圆柱壳在周期性轴向载荷和湿热环境下的非线性参数共振行为。考虑时变轴向载荷、湿热膨胀变形、科里奥利力和离心力以及旋转引起的初始环向张力的影响，基于Love非线性壳理论得到壳的非线性动力学方程，汉密尔顿原理。然后，通过多尺度方法推导出壳稳态响应的解析公式，并通过Routh-Hurwitz准则确定平凡解和非平凡解的稳定性条件。一些数值结果被用来对振动特性进行详细的参数研究，壳的前向和后向行波的幅频响应曲线和不稳定区域。该过程中特别令人感兴趣的是动态轴向载荷和湿热效应对旋转非线性圆柱壳的共振行为的综合影响。