Study on the dynamics of two-degree-of-freedom fractional differential piecewise nonlinear systems under harmonic excitation

• Published in: International journal of non-linear mechanics Vol. 149; p. 104302
• Main Authors: Ma, Wen-Li, Li, Yuan, Wang, Mei-Qi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2023
• Subjects: Fractional differential; IHB method; Nonlinear dynamics; Segmented system; Segmented system; Fractional differential; Nonlinear dynamics; IHB method
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2022.104302

In this paper, a two-degree-of-freedom piecewise nonlinear system model with fractional differential term is constructed. The incremental harmonic balance method (IHB) is used to solve the two-degree-of-freedom piecewise nonlinear system with fractional differential term and the amplitude–frequency curve of the system is obtained. The correctness of the solution of the incremental harmonic balance method is verified by numerical methods. Then the influence of system parameters on the amplitude–frequency response characteristics of the system is studied. The bifurcation diagram of the system is analyzed by numerical method, and the dynamic characteristics of the system under typical parameters are obtained. •A two-DOF piecewise nonlinear system model with fractional differential term is established.•The amplitude–frequency relation equation is obtained by IHB method.•Amplitude–frequency response characteristics under different parameters.•The bifurcation critical value of the model is determined.•The system presents periodic motion, period doubling motion and chaos.