Main resonance analysis of hysteretic nonlinear suspension containing fractional differential

A single degree of freedom dynamical model was initially established for a fractional differential–containing hysteretic nonlinear suspension system under the harmonic excitation of the pavement, and the approximate analytical solution of its forced vibration was obtained through the Krylov–Bogoliubov method. Then, the stability of the stationary solution to the suspension system under the harmonic excitation of the pavement was analyzed. Findings showed that the system's stationary solution was stable. Subsequently, the approximate analytical solution was compared with the amplitude-frequency curve of the numerical solution. The comparative results showed high goodness of fit, verifying the accuracies of the approximate analytical solution and the numerical solution. The bifurcated structural characteristics of the system were also explored according to its amplitude–frequency response. According to the calculation results, the system conformed to the topological structural characteristics of the solution. Finally, the influences and the influence laws of the fractional coefficient and fractional order, the stiffness and damping coefficient of hysteretic nonlinearity on the resonance amplitude, resonance frequency, and nonlinearity degree of the suspension system were analyzed via numerical simulation. (author)