Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force

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.