Nonlinear vibration behaviour and time delay feedback control of graphene reinforced composite cylindrical plates

Chunxia Liu, Ke Jia, Daohang Wang, Lei Zhang and Biyi Zeng

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: This paper primarily investigates the resonance phenomena corresponding to different modes in a graphene-reinforced composite (GRC) cylindrical plate system under time-delay feedback control, external excitation, and 1: 2 internal resonance. To gain a deeper understanding of the system and demonstrate how time delay can be utilized to suppress oscillations in a two-degree-of-freedom nonlinear model. First, the nonlinear differential equations of motion for the system are derived by combining Hamilton's principle and the first-order shear deformation theory (FSDT). The time-delay control equations are obtained using a PD controller. Next, based on the method of multiple scales, the amplitude-frequency response equations are established for the cases of 1: 2 internal resonance and two primary resonances (where the first and second modes are excited separately). Subsequently, the Routh-Hurwitz criterion is employed to derive the necessary and sufficient conditions for the asymptotic stability of the system's steady-state solutions and the occurrence of Hopf bifurcation. Finally, numerical simulations are conducted to integrate theory with computational results. The stability regions, instability regions, and the effects of damping parameters, excitation amplitude, and time-delay parameters on system resonance are discussed for both modes. The analysis reveals that damping parameters and excitation amplitude not only reduce the system's amplitude but also alter the stability regions of non-zero solutions and unstable behaviors such as hard-spring characteristics. The time-delay parameter influences the vibration position, amplitude, and stability of solutions. Optimal ranges for time-delay parameter selection and optimal control strategies for time-delay parameters are provided. The study further unveils the differential regulatory mechanisms of time-delay parameters on dual-mode resonance. The research findings offer theoretical guidance for the practical engineering application of time-delay active control in graphene-reinforced composite structures.

Keywords: Graphene; Composite cylindrical panels; Time delay feedback control; Internal resonance; The multi-scale method; Equilibrium solution (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005521

DOI: 10.1016/j.chaos.2025.116539

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