Nonlinear vibrations of the blade with varying rotating speed

Nonlinear behaviors of thin-walled Euler-Bernoulli beams with varying rotating speed which are attached to a rigid hub are investigated. Centrifugal force, aerodynamic load and the perturbed angular speed due to the inconstant air velocity are considered. The nonlinear factors are involved in displacement-strain relationships. The nonlinear governing partial differential equations of high-speed rotating thin-walled beam are established by using Hamiltonian Principle. Then, the ordinary differential equations of the rotating thin-walled beam are obtained by employing Galekin´s approach during which Galekin´s modes satisfy corresponding boundary conditions. The four-dimensional nonlinear averaged equations are obtained by applying the method of multiple scales. In this paper, the case of 1:1 internal resonance is only considered. The results of the numerical simulation show that there exits complicated nonlinear behaviors in thin-walled Euler-Bernoulli beams with varying rotating speed.