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Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

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  • Alex Elías-Zúñiga
  • Oscar Martínez-Romero

Abstract

The aim of this paper focuses on applying a nonlinearization method to transform forced, damped nonlinear equations of motion of oscillatory systems into the well-known forced, damped Duffing equation. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the amplitude-time, the phase portraits, and the continuous wavelet transform diagrams of the cubic-quintic Duffing equation, the generalized pendulum equation, the power-form elastic term oscillator, the Duffing equation with linear and cubic damped terms, and the pendulum equation with a cubic damped term.

Suggested Citation

  • Alex Elías-Zúñiga & Oscar Martínez-Romero, 2013. "Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jnlmpe:670845
    DOI: 10.1155/2013/670845
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