Nonlinear dynamics of rotating blades with variable cross-section

Abstract

Abstract In this chapter, nonlinear dynamic behaviors of the variable cross-section rotating blades are studied. The blade is considered to be a rotating cantilever plate model with variable cross-section. Considering the influence of centrifugal force, variable rotating speed and cross-section warp. In the light of the Hamilton’s principle, the von Karman deformation theory and the third-order shear deformation theory, we can derive the ordinary differential equation by using Galerkin method from the nonlinear partial differential equations. The multiple scales is applied to get the averaged equations with the 1:3 internal resonance of the rotating blades. Using numerical simulation to study the effects of aerodynamic forces and disturbance amplitude of the rotating blades on nonlinear dynamic behaviors. It shows that the rotating blades performs complex nonlinear dynamic behaviors, such as single periodic, chaotic motions, multiple periodic and quasi-periodic.