A rotating disk linked by a pair of springs

In this paper, we propose a novel model which consists of a rotating disk linked by a pair of springs exhibiting both smooth and discontinuous dynamics. This model provides a cylindrical dynamical system with irrational restoring force due to the geometry configuration. The dynamic behaviors of the unperturbed system are similar to the conventional pendulum coupled with SD oscillator of the homoclinic orbits of the first and second type. A new-type heteroclinic orbit connecting a standard saddle equilibrium and a nonstandard saddle-like equilibrium is presented and investigated analytically in the discontinuous case. Furthermore, the conventional and the extended Melnikov methods are employed to detect the chaotic thresholds for the homoclinic orbits of the first and second type and the heteroclinic-like orbits under the perturbation of both viscous damping and external harmonic forcing for both smooth and discontinuous cases, respectively. The results presented herein this paper demonstrate the predicated periodic solutions and the chaotic attractors of SD type and pendulum type.