Higher Accuracy Approximate Solution for Oscillations of a ... - Core

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stretched elastic wire for which the restoring force for this oscillator has an irrational term with a parameter .... angular frequency of the nonlinear oscillator is ω ...
©Freund Publishing House Ltd. International Journal of Nonlinear Sciences & Numerical Simulation,10(4),493-504,April 2009

Higher Accuracy Approximate Solution for Oscillations of a Mass Attached to a Stretched Elastic Wire by Rational Harmonic Balance Method E. Gimeno, M. L. Álvarez, M. S. Yebra, J. Rosa-Herranz and A. Beléndez Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal. Universidad de Alicante. Apartado 99. E-03080 Alicante. SPAIN E-mail:

[email protected], Fax: +34-96-5909750

Abstract A second-order modified rational harmonic balance method is used for approximately solve the nonlinear differential equation that governs the oscillations of a system typified as a mass attached to a stretched elastic wire for which the restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system. A frequency-amplitude relation is constructed and this frequency is valid for the complete range of oscillation amplitudes A and parameter λ, and excellent agreement of the approximate frequencies with the exact one is demonstrated and discussed. The discrepancy between the approximate frequency and the exact one never exceed 0.12%. This error corresponds to λ = 1, while for λ

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