Subharmonic resonance and chaos for a class of vibration isolation system with two pairs of oblique springs

The subharmonic resonance and chaos are studied in a class of vibration isolation system with two pairs of oblique springs whose stiffness term is a transcendental function. The piecewise linearized systems are established to approximate the vibration isolation system with bistable potential. The homoclinic orbit and periodic orbits for the unperturbed piecewise linearized system are obtained respectively to provide a basis for Melnikov analysis. The thresholds for homoclinic chaos and subharmonic resonance are derived by using non-smooth Melnikov theory, which depend on damping coefficient, frequency and amplitude of excitation. That is, when the system parameters are chosen above the thresholds, the subharmonic resonance and chaos can be avoided in the vibration isolation system. Moreover, the phenomena for infinite subharmonic bifurcations to chaos from odd order subharmonic orbit and the coexistence for chaotic and subharmonic attractors are revealed. The obtained theoretical results are verified through the numerical simulations.