Response analysis of vibro-impact systems under periodic and random excitations

Uncertainties in factors, such as temperature, humidity, and external loads can significantly impact the performance of vibro-impact systems. Effectively managing these uncertainties is essential to ensure the reliability, safety, and performance of engineering systems in real-world operating conditions. This study presents an efficient and straightforward approach to analyze the response of vibro-impact systems subjected to both periodic and random excitations. The method estimates critical noise intensity levels that lead to dangerous noise-induced bifurcations by utilizing confidence ellipses and the global structure of the deterministic system. Furthermore, the most probable locations for stochastic attractor jumps are identified based on the evolution of the maximum eigenvalue of the stochastic sensitivity function over one period of excitation. The proposed method is validated through the analysis of both single- and two-degree-of-freedom impact oscillators. These findings provide a robust framework for predicting complex dynamic behaviors, thereby enhancing the design and application of vibro-impact systems across various engineering fields.