An analytical solution for nonlinear dynamics of a viscoelastic beam-heavy mass system †

摘要: The aim of this study is to develop an approximate analytic solution for nonlinear dynamic response a simply-supported Kelvin- Voigt viscoelastic beam with attached heavy intra-span mass. A geometric nonlinearity due midplane stretching considered and Newton's second law motion along Kelvin-Voigt rheological model, which two-parameter energy dissipation are employed derive the equations motion. method multiple timescales applied directly governing motion, natural frequencies vibration responses system obtained analytically. Regarding resonance case, limit-cycle formulated parametric conducted in order highlight influences parameters. main objective examine how plain (i.e. without additional adornment) modified by presence mass, somewhere length.