Non-linear dynamic response of a rotating thin-walled composite beam

Abstract

The nonlinear planar response of a cantilever rota ting slender beam to a principal parametric resonance of its first bending mode is analyzed. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of sma ll strains. The beam is subjected to a harmonic transverse load in the presence of in ternal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady stat e responses and their stability. Amplitude and phase modulation equations as well as external force–r esponse and frequency–response curves are obtained. Numerical simulations show a complex dynamic scenario and detect chaos and unbounded motions in the instability regions of the periodic solutions.