Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

Alex Elías-Zúñiga and Oscar Martínez-Romero

Mathematical Problems in Engineering, 2013, vol. 2013, 1-9

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:574696

DOI: 10.1155/2013/574696

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