Internal resonance of an axially transporting beam with a two-frequency parametric excitation

Abstract This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by speed perturbation. The Kelvin-Voigt model is introduced to describe characteristics beam. governing equation and associated boundary conditions are obtained Newton’s second law. method multiple scales utilized obtain steady-state responses. Routh-Hurwitz criterion used determine stabilities bifurcations effects material coefficient on dynamics studied in detail series numerical demonstrations. Interesting phenomena responses revealed excitation. approximate analytical validated via differential quadrature method.