Nonlinear Dynamics of Rotating Pretwisted Cylindrical Panels Under 1:2 Internal Resonances

Abstract

This paper investigates the nonlinear vibrations of the rotating pretwisted cylindrical panel under higher-frequency primary resonance and lower-frequency primary resonance for the case of 1:2 internal resonances. An accurate strain-displacement relationship is derived by the Green strain tensor. First-order shear deformation theory and Hamilton principle are utilized to establish the partial differential governing equation of the rotating cylindrical panel. Galerkin approach is employed to obtain the two-degree-of-freedom nonlinear system, which contains coupling between linear stiffness terms of the two transverse modes. The method of multiple scales is used to obtain the modulation equations for the amplitudes and phases. Numerical simulations are performed to show amplitude-frequency responses and bifurcation behaviors of the system. Two types of numerical methods are compared to describe the amplitude-frequency responses of the system. The results show the accuracy of our proposed method. The effects of the detuning parameter, the damping coefficient and the excitation amplitude on amplitude-frequency responses and bifurcation behaviors are fully discussed.