Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 85, Issue -, Pages 197-206Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2016.06.008
Keywords
Nonlinear oscillator; Non-harmonic periodic loading; Jacobi elliptic functions; Exact analytical frequency-amplitude relation
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The steady-state response of an undamped Duffing oscillator to periodic external forces is studied. The forcing functions are chosen such that the time course of the displacement can be described by exact analytical expressions. The displacement and forcing functions are governed by Jacobi elliptic functions and thus are periodic but generally non-harmonic. The parameter of the elliptic functions is deliberately chosen. For certain parameter choices, exact analytical expressions are found for the frequency-amplitude relation. (C) 2016 Elsevier Ltd. All rights reserved.
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