NON-LINEAR NORMAL MODES OF A ROTATING BEAM

MACHADO SEBASTIÁN PABLO; SARAVIA CESAR MARTÍN

Bahia Blanca

Congreso; Tercer Congreso de Matemática Aplicada, Computacional e Industrial, III MACI 2011.; 2011

Asociación Argentina de Matemática Aplicada, Computacional e Industrial, ASAMACI

Non-linear normal modes of vibration for a cantilever rotating beam are evaluated considering the continuous system in external and internal resonance conditions. The equation of motion is obtained in the form of an integropartial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. 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 state responses and their stability. Comparisons between different models (using linear and non-linear modes) are also provided. Numerical simulations show a complex dynamic scenario and detect chaos and unbounded motions in the instability regions of the periodic solutions.