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

摘要

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. (C) 2016 Elsevier Ltd. All rights reserved.