Nonlinear Resonance Behaviors of Rotating Pretwisted Cylindrical Panels

Abstract

The rotating blade is simplified as a rotating cylindrical panel with a presetting angle and a pretwist angle. Nonlinear dynamic behaviors of the rotating cylindrical panel under higher-frequency primary resonance and lower-frequency primary resonance in the presence of 1:2 internal resonance are discussed. We use the Green strain tensor to derive an strain-displacement relationship. Based on the first-order shear deformation theory, Hamilton principle and Galerkin method is utilized to acquire nonlinear ordinary differential equations of the system, which contains coupling between linear stiffness terms of the two transverse modes. The modulation equations are obtained by using the method of multiple scales. Matcont package is used to portray frequency-amplitude response curves and force-amplitude response curves of the system under higher-frequency primary resonance and lower-frequency primary resonance.