Quasi-periodic motion is an oscillation of a dynamic system characterized by m frequencies that are incommensurable with one *** this work,a new incremental harmonic balance(IHB)method with only two time scales,where ...
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Quasi-periodic motion is an oscillation of a dynamic system characterized by m frequencies that are incommensurable with one *** this work,a new incremental harmonic balance(IHB)method with only two time scales,where one is one of the m frequencies,referred to as a fundamental frequency,and the other is an interval distance of two adjacent frequencies,is proposed for quasi-periodic motions of an axially moving beam with three-to-one internal resonance under single-tone external *** is found that the interval frequency of every two adjacent frequencies,located around the fundamental frequency or one of its integer multiples,is fixed due to nonlinear coupling among resonant vibration ***,only two time scales are used in the IHB method to obtain all incommensurable frequencies of quasi-periodic motions of the axially moving *** present IHB method can accurately trace from periodic responses of the beam to its quasi-periodic *** periodic responses of the axially moving beam,the single fundamental frequency is used in the IHB method to obtain *** quasi-periodic motions of the beam,the present IHB method with two time scales is used,along with an amplitude increment approach that includes a large number of harmonics,to determine all the frequency *** the frequency components and their corresponding amplitudes,obtained from the present IHB method,are in excellent agreement with those from numerical integration using the fourth-order Runge-Kutta method.
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