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Mathematical Problems in Engineering
Volume 2013, Article ID 574696, 9 pages
Research Article

Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

Departamento de Ingeniería Mecánica, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico

Received 16 February 2013; Revised 4 May 2013; Accepted 10 May 2013

Academic Editor: Miguel A. F. Sanjuán

Copyright © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.