Amplitude-frequency characteristics and diversity of periodic motions of fractional-order nonlinear vibration isolation system with constant excitation

The fractional nonlinear Zener model is used to describe the nonlinear and viscoelastic constitutive relation of the vibration isolation system. The variation law of system amplitude-frequency response and backbone under the combined action of constant excitation and harmonic excitation is discussed, and the influence of constant excitation on the dynamic behavior of vibration isolation system is discussed significantly. The fractional-order derivative term is made equivalent to a term in the form of trigonometric function, the steady-state response of the system is solved by Harmonic Balance method, and the results are compared with a variety of other methods. The influences of different parameters on the coexistence frequency band range of the amplitude-frequency response multi-state solution are summarized, and the dynamic behaviors of the system under the combined excitation are obtained by using numerically simulation. The results show that there are five solutions co-existence region in the amplitude-frequency response solution under the combined effect of constant excitation and harmonic excitation, and the system shows a phenomenon of coexistence of softening characteristic and hardening characteristic, and the backbone of the amplitude-frequency curve is tilted firstly to the left and then to the right. Additionally, it is found that the periodic motion and chaos coexist in the system under the combined excitation, and the transition laws of the polymorphic coexistence region and its adjacent regions are summarized explicitly. Affected by constant excitation, the diversity of periodic motion of the system under the combined excitation is significantly different from the dynamic behavior under the action of simple harmonic excitation alone, and the transition rules of periodic motion of the system under the action of combined excitation are summarized based on the Lyapunov exponent.