Beléndez, Augusto, Gimeno, Encarnación, Beléndez, Tarsicio, Hernández Prados, Antonio
Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation
BELÉNDEZ VÁZQUEZ, Augusto et al. “Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation". Mechanics Research Communications. Vol. 36, Issue 6 (Sept. 2009). ISSN 0093-6413, pp. 728-734
URI: http://hdl.handle.net/10045/11911
DOI: 10.1016/j.mechrescom.2009.03.001
ISSN: 0093-6413 (Print)
Abstract: 
A second-order modified rational harmonic balance method is used to approximately solve the nonlinear differential equation that governs the oscillations of a conservative autonomous system with one degree of freedom. The Duffing oscillator is analyzed to illustrate the usefulness and effectiveness of the proposed technique. We find that this method works very well for this oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second-order approximation we have shown that the relative error in the analytical approximate frequency is as low as 0.0055% when A tends to infinity. We also compared the Fourier series expansions of the analytical approximate solution and the exact one. This has allowed us to compare the coefficients for the different harmonic terms in these solutions.
Keywords:Nonlinear oscillators, Approximate solutions, Rational harmonic balance method, Duffing oscillator
Elsevier
info:eu-repo/semantics/article