Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire

Authors:
Seher Durmaz;Sezgin Altay Demirbağ;Metin Orhan Kaya
Affiliations:
Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey;Faculty of Science and Letts, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey;Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented. At the beginning of the study, the equation of motion is derived in a detailed way. He's max-min approach, He's frequency-amplitude method and the parameter-expansion method are implemented to solve the established model. The numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations, and a very good agreement is observed. The relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results.