Analytical and numerical investigations of stable periodic solutions of the impacting oscillator with a moving base

作者：Czolczynski Krzysztof; Blazejczyk Okolewska Barbara^*; Okolewski Andrzej

来源：International Journal of Mechanical Sciences, 2016, 115: 325-338.

DOI：10.1016/j.ijmecsci.2016.07.004

• Impact oscillator
• Time-varying amplitude constraint
• Stable periodic solutions
• Lyapunov exponents
• Hard versus soft impact

A vibrating system with impacts that can be used as a model of the cantilever beam with a mass at its end impacting against a harmonically moving frame is investigated. An analytical method, based on Peterka's approach, to obtain stable periodic solutions to the equations of motion is presented. The results of analytical investigations have been compared to the results of numerical simulations conducted for two different, equivalent as far as the impact energy dissipation extent is concerned, ways of modelling of impacts. The ranges of existence of stable periodic solutions, determined analytically and numerically with bifurcation diagrams of spectra of Lyapunov exponents, show excellent conformity.

• 出版日期2016-9