Abstract
Nonlinear vibrations of a cantilevered slender beam in case of internal resonance are investigated. We adopt the equations of motion of horizontal bending, vertical bending and torsion based on HodgesDowell beam theory. To find the conditions of internal resonance, we use the method of multiple scales to directly attack the partial-differential equations and the associated boundary conditions. We obtain the conditions of natural frequencies under which internal resonance may occur. The free vibrations of the beam with the presence of internal resonance are investigated. We obtained the equations governing the modulation of amplitudes and phases. After that, we consider the internal resonance in the beam model when one of the torsional modes involved in the internal resonance is excited by a primary resonance. The numerical results show that energy transfers among different modes of motion through nonlinear interactions.
Published Version
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