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.

在本文中，我们研究了在两个频率的准周期强迫下细长刚性摇动块中奇怪的非混沌吸引子（SNA）的存在。我们发现SNA可以存在于准周期吸引子和混沌吸引子之间，或者两个混沌吸引子之间。特别是，我们证明了准周期吸引子的环面加倍分叉可以在转变为混沌吸引子之前通过分形路径产生 SNA。这种现象在准周期强迫不连续微分方程和振动冲击系统中很少有报道。 SNA 的属性通过 Lyapunov 指数、有理逼近、相位灵敏度、功率谱和附近轨迹的分离来验证。