Title: Modelling and experimental investigations on the geometrical nonlinear dynamics of the SD oscillator

Authors: Enli Chen; Bogang Chu; Yang Wang

Addresses: School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei 050043, China ' School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei 050043, China ' School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei 050043, China

Abstract: In this paper, an experimental rig and a dynamic model for the smooth and discontinuous (SD) oscillator is set up to describe the geometrical nonlinearity caused by large deformation, which is typical of irrational nonlinearity with double stabilities. The system parameters of the proposed device are adjustable and measurable during the experiment for different working conditions. Various experimental investigations under the harmonic excitation are carried out to explore the complex nonlinear behaviour of periodic solution, bifurcation phenomenon, chaotic phenomena and the transitions among the multiple motion patterns. Numerical simulations are carried out to demonstrate the reliability of the proposed experimental rig, showing a good agreement with presented experimental results. The results presented via experimental investigations reflect the natural behaviour of the geometrical nonlinear dynamics.

Keywords: SD oscillators; nonlinear behaviour; experimental parameter recognition; nonlinear experiment rig; geometrical nonlinearity; irrational nonlinearity; bifurcation; chaos; spectrum; Poincare section; dynamic modelling; nonlinear dynamics; smooth and discontinuous oscillators; harmonic excitation; numerical simulation.

DOI: 10.1504/IJMIC.2016.075813

International Journal of Modelling, Identification and Control, 2016 Vol.25 No.3, pp.190 - 198

Received: 21 Feb 2015
Accepted: 02 Jun 2015
Published online: 06 Apr 2016 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article