Analysis of non-linear autonomous conservative oscillators by a time transformation method |
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Authors: | T.D. Burton M.N. Hamdan |
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Affiliation: | Department of Mechanical Engineering, Washington State University, Pullman, Washington 99164-2920, U.S.A. |
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Abstract: | The problem considered is that of the free vibration of the class of strongly non-linear oscillators ü + mu + αf(u) = 0, where m = 1, 0 or ?1, f(u) is a non-linear function of the displacement u(t), and α is not small. Through a continuous stretching of the time t a new time T is found in whose domain the response is simple harmonic. This time transformation method allows the response u(t) and period τ to be calculated to any desired degree of accuracy; however, the primary objective is to develop reasonably simple, accurate approximations for the oscillators considered. |
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