Grazing bifurcations in an elastic structure excited by harmonic impactor motions

• Published in: Physica. D Vol. 237; no. 8; pp. 1129 - 1138
• Main Authors: Long, X.-H., Lin, G., Balachandran, B.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.06.2008; Elsevier
• Subjects: Elastic structure; Exact sciences and technology; Grazing bifurcation; Impact dynamics; Non-linear dynamics; Physics; 46.40.-f; Impact dynamics; Grazing bifurcation; 05.45.Pq; 0.5.45-a; 46.70.-p; Elastic structure; Non-linear dynamics; Poincaré mapping; Degrees of freedom; Digital simulation; Bifurcation; Periodic orbit; Non linear phenomenon; Oscillators; Dynamics; Models; Excitation
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2007.12.001

In this article, non-smooth dynamics of an elastic structure excited by a harmonic impactor motion is studied through a combination of experimental, numerical, and analytical efforts. The test apparatus consists of a stainless steel cantilever structure with a tip mass that is impacted by a shaker. Soft impact between the impactor and the structure is considered, and bifurcations with respect to quasi-static variation of the shaker excitation frequency are examined. In the experiments, qualitative changes that can be associated with grazing and corner-collision bifurcations are observed. Aperiodic motions are also observed in the vicinity of the non-smooth bifurcation points. Assuming the system response to be dominated by the structure’s fundamental mode, a non-autonomous, single degree-of-freedom model is developed and used for local analysis and numerical simulations. The predicted grazing and corner-collision bifurcations are in agreement with the experimental results. To study the local bifurcation behavior at the corner-collision point and explore the mechanism responsible for the aperiodic motions, a derivation is carried out to construct local Poincaré maps of periodic orbits at a corner-collision point such as the one observed in the soft-impact oscillator.