Abstract
Piecewise asymmetric oscillators are a type of strongly nonlinear system characterized by asymmetric stiffness coefficients, leading to complex dynamical behavior. This paper investigates the global dynamics of a class of piecewise asymmetric oscillators under periodic excitation. Using the non-smooth Melnikov method, the threshold conditions for existence of Smale horseshoe chaos and subharmonic resonances are derived. The theoretical results are validated through time history portraits, phase portraits, Poincaré sect portraits, and maximum Lyapunov exponent. Additionally, the effects of damping, spring stiffness, and frequency of the external excitation on chaotic motion are analyzed. Furthermore, multistable behavior of the system and the basins of attraction corresponding to coexisting attractors are also discussed.
