Abstract: A nonlinear analysis of the response of a simply-supported viscoelastic buckled beam to a couple of constant axial force and harmonic excitation is resented. The disturbance equation of transverse vibration of the buckled beam is derived from the free governing equation via a coordinate transform. The Galerkin method is applied to truncate the systems to a multiple degrees-of-freedom of nonlinear vibration system. In the presence of internal resonances, a method of multiple scales is developed to obtain the steady-state relationship between the amplitudes in the first two resonant modes in weak forced, and reveal a unique saturation phenomenon in nonlinear system with quadratic items.

Key words: amplitude-frequency characteristics, buckled, forced vibration, saturation phenomenon, viscoelastic beam, nonlinear