Singular closed orbits and chaotic behavior of a double-winged quasi-zero-stiffness system

The complex chaotic behavior of a quasi-zero-stiffness (QZS) double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations. The analysis reveals the coexistence of multiple attractors. As a key mass parameter varies, the mechanism underlying degenerate singular closed orbits is elucidated, based upon which five distinct types of singular closed orbits are discovered, exhibiting both smooth and discontinuous (SD) characteristics. The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations. The numerical results further demonstrate the coexistence of SD motions. For zero damping systems, the Kolmogorov-Arnold-Moser (KAM) structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions. These findings advance the understanding of chaotic dynamics in non-smooth multi-well impact systems.