Abstract This paper investigates the complex nonlinear vibrations and internal resonance of the rotating blade subjected to the aerodynamic force, which is simplified to a pretwisted rotating cantilever rectangular plate with the varying cross-section and varying rotating speed. Considering the effects of the cross-section warping, pretwisted and presetting angles, the nonlinear partial differential governing equations of motion are established based on the third-order shear deformation theory, von Karman large deformation theory and Hamilton principle. Two-degree-of-freedom nonlinear ordinary differential equations of motion are obtained by using Galerkin method. The method of multiple scales is applied to obtain the averaged equations under the case of the primary parametric resonance-1/2 subharmonic resonance and 1:2 internal resonance. Numerical simulations are performed to portray the amplitude-frequency response and amplitude-force response curves, bifurcations and chaotic dynamics of the pretwisted rotating cantilever rectangular plate by discussing the influences of the aerodynamic force and rotating speed perturbation. The bifurcation diagrams, maximum Lyapunov exponents, phase portraits, waveforms and Poincare maps are utilized to illustrate the complex nonlinear vibrations of the pretwisted rotating cantilever rectangular plate.

中文翻译：

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变截面和变气动力预扭旋转悬臂矩形板的非线性振动与内共振

摘要 本文研究了旋转叶片在空气动力作用下的复杂非线性振动和内共振，将其简化为具有变截面和变转速的预扭旋转悬臂矩形板。考虑截面翘曲、预扭和预置角的影响，基于三阶剪切变形理论、von Karman大变形理论和Hamilton原理，建立了非线性偏微分运动控制方程。利用伽辽金法得到二自由度非线性常微分运动方程。应用多尺度方法得到主参数谐振-1/2次谐波谐振和1:2内谐振情况下的平均方程。数值模拟通过讨论气动力和转速扰动的影响，刻画了预扭旋转悬臂矩形板的幅频响应和幅力响应曲线、分岔和混沌动力学。利用分岔图、最大李雅普诺夫指数、相图、波形和庞加莱图来说明预扭旋转悬臂矩形板的复杂非线性振动。