Multiscale analysis of nonlinear oscillations of an axially travelling viscoelastic string

摘要

This paper deals with the steady-state transverse vibration of parametrically excited axially moving string with geometric nonlinearity. The material of the string is assumed to obey the Boltzmann superposition principle. Based on the equation of motion, the method of multiple scales is applied to establish the solvability condition. The amplitude and the existence conditions of nontrivial steady-state response of the summation resonance are presented.