Mergen H. Ghayesh*, Farbod Alijani and Mohammad A. Darabi
The Journal of Mechanical Science and Technology, vol. 25, no. 8, pp.1915-1923, 2011

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

Keyword : Nonlinear dynamics; Kelvin-Voigt viscoelastic material; Method of multiple timescale