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Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

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  • Alex Elías-Zúñiga
  • Oscar Martínez-Romero

Abstract

We study the dynamical response of an asymmetric forced, damped Helmholtz-Duffing oscillator by using Jacobi elliptic functions, the method of elliptic balance, and Fourier series. By assuming that the modulus of the elliptic functions is slowly varying as a function of time and by considering the primary resonance response of the Helmholtz-Duffing oscillator, we derived an approximate solution that provides the time-dependent amplitude-frequency response curves. The accuracy of the derived approximate solution is evaluated by studying the evolution of the response curves of an asymmetric Duffing oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.

Suggested Citation

  • Alex Elías-Zúñiga & Oscar Martínez-Romero, 2013. "Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, June.
    • Handle: RePEc:hin:jnlmpe:574696
    DOI: 10.1155/2013/574696
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