Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam

Nonlinear amplitude-frequency response, unstable boundary and dynamic responses of an axially moving viscoelastic sandwich beam under low-and high-frequency principle resonances are discussed and compared in this paper, respectively. Governing equation for transverse vibration of the axially moving viscoelastic sandwich beam, a nonlinear partial differential equation, is transformed into nonlinear ordinary differential equations using the method of Galerkin truncation, afterwards the complex eigenfunctions of the system is obtained adopting the method of multiple scales. Then, the tuning equations are derived and the stability conditions of nontrivial solutions are analyzed employing the Routh-Hurwitz criterion. Finally, detailed parametric studies on present results are numerically carried out, including thickness of the core layer, mean velocity, initial tension, and amplitude of the external excitation. (C) 2018 Elsevier Ltd. All rights reserved.