Effect of the Impact Model on the Dynamics of a Vibro-Impact System with Non-Ideal Excitation

Abstract

The influence of the impact model on the dynamic behavior of a vibro-impact system with non-ideal excitation is analyzed in this paper. The system consists of a crank-slider mechanism and an oscillator, and its mathematical model is derived using Lagrange’s equations of motion. Three soft impact models (Spring-Damper, Hertz, and Brake) and one hard impact model (Newton) are considered. The system response is analyzed numerically using frequency response diagrams, phase portraits, displacement-time histories, and basins of attraction. Three response regions are identified for all four models: non-impact, impact, and multiple solution regions. The multiple solution region corresponds to excitation-parameter values for which the system response depends on the initial conditions. For all models, the non-impact regime occurs for , while the impact regime occurs for . The largest differences between the models occur in the multiple solution region. Its upper boundary is  for the Newton model,  for the Spring-Damper model, and  for the Hertz and Brake models. At lower values of the excitation control parameter, all four models predict similar dynamic responses, whereas noticeable differences emerge at higher values. These results demonstrate that impact-model selection becomes increasingly important at higher excitation levels for accurately predicting the system response and its sensitivity to initial conditions.