Nonlinear dynamic response of a rotating thin-walled composite beam

MACHADO, SEBASTIÁN PABLO; SARAVIA, CÉSAR MARTÍN

Buenos Aires

Congreso; CILAMCE/MECOM 2010 - Iberian-Latin-American Congress on Computational Methods in Engineering; 2010

Asociación Argentina de Mecánica Computacional

The nonlinear planar response of a cantilever rotating 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 small strains. The beam is subjected to a harmonic transverse load in the presence of internal 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 state responses and their stability. Amplitude and phase modulation equations as well as external force?response 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.