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Forced harmonic vibrations of duffing oscillator with cubic-quintic spring nonlinearity

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  • Kuznetsov, Sergey V.

Abstract

The modified Duffing oscillator with cubic-quintic nonlinearity at harmonic force excitations is analysed. Several phenomena are observed, including (i) the possibility for the presence of triple wells in the potential energy; (ii) the finding of a relation between the roots of the potential and nonlinear elastic moduli; (ii) the appearance of two chaotic regimes split by a regular regime; (iii) the occurrence of harmonic and superharmonic oscillations in the regular regime; and (iv) a significant topological difference in the Poincaré sections associated with these chaotic regimes. These observations open the possibility of creating a new type of vibration isolation devices free from viscous or dry friction elements. The analysis is based on constructing potential and solving the equations of motion by the finite difference method in combination with the multiprecision package for long-mantissa computations, enabling stable computations over large time intervals.

Suggested Citation

  • Kuznetsov, Sergey V., 2025. "Forced harmonic vibrations of duffing oscillator with cubic-quintic spring nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s096007792500712x
    DOI: 10.1016/j.chaos.2025.116699
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    References listed on IDEAS

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    1. S. A. El-Tantawy & Alvaro H. Salas & M. R. Alharthi, 2021. "On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, February.
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    6. Valentine Aleksandrovich Kim & Roman Ivanovich Parovik & Zafar Ravshanovich Rakhmonov, 2023. "Implicit Finite-Difference Scheme for a Duffing Oscillator with a Derivative of Variable Fractional Order of the Riemann-Liouville Type," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
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    1. Li, Jing & Wang, Yongchun & Liu, Di, 2026. "Transient response analysis of nonlinear systems under combined nonstationary and stationary noise excitations: An improved complex fractional moment method," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).

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