Abstract
To analyze the piecewise non-linear system with fractional order differentiation, fractional-order was introduced into the two piecewise systems to accurately describe the stress relaxation of viscoelastic materials. A non-linear dynamic model with non-linear stiffness, damping, and fractional-order multipiece wise points was also established. Under periodic excitation, the equation of the non-linear system relationship in the system was obtained using the average method, where the amplitude-frequency response characteristics under different damping, stiffness, and fractional order parameters were provided. The influence of non-linear factors and fractional order terms on the stability of the system was studied. The chaotic behavior of the system under different parameter disturbances was determined, and the results indicate that the system presents chaotic behavior with the change in disturbance parameters. Moreover, the decreased linear damping subjects the system to a wider range of chaotic states.
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