A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation
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Date
2010
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Abstract
A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. © 2010 Elsevier Ltd. All rights reserved.
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Resonance , Approximate analytical solutions , Continuous system , Cubic nonlinearities , Euler Bernoulli beams , External excitation , Forced vibration , General solutions , Internal resonance , Method of multiple scale , Primary resonance , Solution algorithms , Specific problems , Steady state solution , Vibrational models , Viscoelastic beams , Mathematical operators