Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus

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 dam ping, 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.(c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces the use of fractional order differentiation to accurately describe the stress relaxation behavior of viscoelastic materials and establishes a non-linear dynamic model. By studying the influence of non-linear factors and fractional order terms on the stability of the system, it is found that the system exhibits chaotic behavior under different parameter disturbances, and reducing linear damping widens the range of chaotic states the system can exhibit.