Beléndez, Augusto, Arribas Garde, Enrique, Francés, Jorge, Pascual, Inmaculada
Comments on ‘A finite extensibility nonlinear oscillator’
BELÉNDEZ VÁZQUEZ, Augusto, et al. "Comments on ‘A finite extensibility nonlinear oscillator’". Applied Mathematics and Computation. Vol. 218, Issue 10 (Jan. 2012). ISSN 0096-3003, pp. 6168–6175
URI: http://hdl.handle.net/10045/20424
DOI: 10.1016/j.amc.2011.12.012
ISSN: 0096-3003 (Print)
Abstract: 
The aim of this comment is to provide more information about the study of the dynamics of a finite extensibility nonlinear oscillator conducted by Febbo [M. Febbo, A finite extensibility nonlinear oscillator, Applied Mathematics and Computation 217 (2011) 6464–6475]. We show that the linearized harmonic balance method is not sufficiently adequate for this oscillator and that the harmonic balance method (HBM) without linearization provides better results. We also discuss what happens when the oscillation amplitude approaches 1 and why the harmonic balance method does not give optimum results. For these values of the oscillation amplitude the periodic solution becomes markedly anharmonic and is almost straight between x = +A and x = −A (with negative slope) and between x = −A and x = +A (with positive slope). Finally, a ‘heuristic’ solution is proposed which is adequate for the whole amplitude range 0 < A < 1, which is consistent with the approximate solution obtained previously for A < 0.9 using the HBM.
Keywords:Finite extensibility, Nonlinear oscillator, Approximate solutions, Harmonic balance method
Elsevier
info:eu-repo/semantics/article