Resonance study of fractional-order strongly nonlinear duffing systems

This article takes a class of strongly nonlinear Duffing systems with fractional-order terms as the research object, studying their main resonance and conditions for chaos under single-frequency excitation. The approximate analytical solution of the main resonance of the system under single-frequency excitation is obtained by the multi-scale method. The approximate analytical solution is utilized to construct the steady-state motion's amplitude–frequency response equation, and Lyapunov's first method is used to determine the constant solution's stability condition, which is then used to analyze the steady-state motion's stability. The system is examined by using the Melnikov method to identify the circumstances that would appear to result in a transverse intersection of heterodox orbits and the onset of chaos in the system. The amplitude–frequency characteristics of the total response of the system at various excitation frequencies are investigated in numerical simulations using analytical and simulation methods, respectively, and the system makes a comparison of amplitude–frequency curves, confirming that the numerical results and results achieve a consistent trend. The effects of nonlinear stiffness coefficients, excitation amplitude, fractional-order differential term order and fractional-order differential term coefficients on the system's amplitude–frequency response are each examined in turn. A numerical investigation of the effects of system parameters on chaotic motion is then conducted using many kinds of diagrams .