Galerkin method for steady-state response of nonlinear forced vibration of axially moving beams at supercritical speeds

► Nonlinear forced vibration of supercritically moving viscoelastic beams is studied. ► Galerkin method is used to analyze the governing equation. ► Frequency-response curves are obtained via the multiple-scale method. ► Approximate results are numerically verified via the finite different schemes.