Abstract
An averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non-linear oscillators ẍ + g(x) = εƒ(x, ẋ) and ẍ + g(x) = εF(x, ẋ, Ωt), where g(x) is an arbitrary non-linear function. The method gives the approximate solutions in terms of generalized harmonic functions. These functions are also periodic and are exact solutions of strongly non-linear differential equations. Some phenomena considered include limit cycles of strongly non-linear autonomous oscillators and steady state response of strongly non-linear oscillators subject to weak harmonic excitation. The procedure is simple and easy to apply.
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