Harmonic balance approach to periodic solutions of non-linear jerk equations
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The method of harmonic balance is applied to non-linear jerk equations, which involve the third order time-derivative. For many types of cubic non-linearities, the method yields good estimates of the period and displacement amplitude of oscillations for a range of values of initial velocity amplitude when compared with numerical solutions. Some limitations, notably the restriction to zero initial acceleration, as well as implications and possible extensions are discussed.
Journal of Sound and Vibration
© 2004 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.