Melnikov-type method for chaos in a class of hybrid piecewise-smooth systems with impact and noise excitation under unilateral rigid constraint

The Melnikov method for chaos is developed in a class of hybrid piecewise-smooth systems with impact and noise excitation under unilateral rigid constraint, the corresponding unperturbed Hamiltonian system has the three-piecewise homoclinic orbit. This homoclinic orbit crosses the first and second switching manifolds continuously, then jumps symmetrically with x-axis on the third switching manifold through the rigid impact. It will not cross the third switching manifold and enter the next zone under unilateral rigid constraint. Especially, the perturbed trajectory crosses the first switching manifold through the elastic impact rule expressed by the reset map. Afterwards, the random non-smooth Melnikov function is obtained, the chaotic criteria with and without noise excitation are derived. Furthermore, the theoretical results obtained are applied to analyse the chaos in an actual non-smooth mechanical system with impacts, dry friction and noise excitation.& COPY; 2023 Elsevier Inc. All rights reserved.