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Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type

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  • Cveticanin, L.

Abstract

In this paper, an approximate analytic procedure is developed for solving the strong non-linear differential equations of the Duffing type with complex-valued function which describes the dynamical behavior of many real systems. The method is based on the elliptic-Krylov–Bogolubov procedure where the solutions are the Jacobi elliptic functions. As an example, the self-excited vibrations of the rotor with variable shaft rigidity are considered. The analytical results of this example are compared with numerical ones and excellent agreement is found between them.

Suggested Citation

  • Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    • Handle: RePEc:eee:phsmap:v:297:y:2001:i:3:p:348-360
    DOI: 10.1016/S0378-4371(01)00228-X
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    References listed on IDEAS

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    1. Mahmoud, Gamal M., 1997. "Stability regions for coupled Hill's equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 239-249.
    2. Mahmoud, Gamal M., 1998. "Approximate solutions of a class of complex nonlinear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 211-222.
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    Cited by:

    1. Cveticanin, L., 2003. "Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 83-94.
    2. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    3. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2023. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    4. Xu, Yong & Xu, Wei & Mahmoud, Gamal M., 2008. "On a complex Duffing system with random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 126-132.
    5. Xu, Yong & Xu, Wei & Mahmoud, Gamal M, 2004. "On a complex beam–beam interaction model with random forcing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 347-360.
    6. Xu, Yong & Zhang, Huiqing & Xu, Wei, 2007. "On stochastic complex beam–beam interaction models with Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 259-272.

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