Periodic motions and transition phenomena in a two-degrees-of-freedom system with perfectly plastic impact

✍ Scribed by G.W. Luo

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 321 KB
• Volume: 263
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00496-x

✦ Synopsis

A two-degrees-of-freedom vibratory system with a constraint is considered. The constraint leads motions with impacts. Such models play an important role in the studies of mechanical systems with amplitude constraining stops. On the perfectly plastic impact condition, the dynamics of the vibro-impact system are represented by a three-dimensional map, which is of piecewise property and singularities caused by the motions with grazing boundary. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated. The vibro-impact system goes through complicated dynamic evolution beyond period-doubling bifurcations with an increase in excitation frequency. Period-doubling bifurcations of period n single-impact orbits of the map are commonly existential, but the period-doubling cascades do not occur because of the singularities of the map. The motions with grazing boundary lead complex sequences of transitions to chaos.