Numerical analysis of a vibro-impact system with ideal and non-ideal excitation

Abstract

This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system can be exposed to ideal or non-ideal excitation. The impact occurs during the motion of the oscillator when it hits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibro-impact systems with ideal and non-ideal excitation are analysed. For these system differential equations are formed and the impact model is provided in the paper. The impact causes a strong nonlinearity in the system. The mathematical model of the vibro-impact system with ideal excitation is presented as a second order differential equation where the vibro-impact system with non-ideal excitation is given as a coupled system of nonlinear second order differential equations. Numerical simulations are carried out for the two systems and the results obtained are shown in terms of frequency response diagrams as well as in terms of time-displacement diagrams. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For a specific value of the excitation frequency in the frequency response diagram where multiple solutions are found, basin of attractor diagrams are formed. Average value of the excitation frequency is used for the vibro-impact system with non-ideal excitation.