Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-01, Vol.154, p.111626, Article 111626
• Main Authors: Mei-Qi, Wang, Wen-Li, Ma, En-Li, Chen, Yu-Jian, Chang, Cui-Yan, Wang
• Format: Article
• Language: English
• Subjects: Average method; Bifurcation theory; Fractional calculus; Piecewise nonlinear dynamics
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111626

•In this paper, a dynamic system with fractional-order and travel elastic constraints is considered, and a multi-stage fractional dynamic model with nonlinear stiffness and damping is established.•The amplitude-frequency relationship equation of the system is obtained by the averaging method under periodic excitation. The amplitude-frequency response characteristics under different parameters are given. The influence of nonlinear factors and fractional-order terms on system stability is studied.•The bifurcation behavior of the system under different external disturbances is analyzed, thus system presents a variety of motion states such as periodic motion, period-doubling motion, and chaos with change in disturbance parameters.•The phase diagram, Poincare interface diagram and cell mapping of the system under different external disturbances are analyzed. 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.