Strange Nonchaotic Attractors in a Quasiperiodically Excited Slender Rigid Rocking Block with Two Frequencies

In this paper, we investigate the existence of strange nonchaotic attractors (SNAs) in a slender rigid rocking block under quasi-periodic forcing with two frequencies. We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor, or between two chaotic attractors. In particular, we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors. This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems. The properties of SNAs are verified by the Lyapunov exponent, rational approximation, phase sensitivity, power spectrum, and separation of nearby trajectories.