Open AccessParametrically excited nonlinear systems: a comparison of two methods
Author(s) -
A.F. El-Bassiouny
Publication year - 2002
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/s0161171202007019
Subject(s) - mathematics , nonlinear system , parametric statistics , resonance (particle physics) , ordinary differential equation , multiple scale analysis , stability (learning theory) , amplitude , mathematical analysis , synchronization (alternating current) , steady state (chemistry) , excited state , control theory (sociology) , differential equation , physics , topology (electrical circuits) , quantum mechanics , statistics , chemistry , control (management) , management , machine learning , combinatorics , computer science , economics
Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in thepresence of three-to-one internal resonance is investigated. Twoapproximate methods (the multiple scales and the generalizedsynchronization) are used to construct a first-order nonlinearordinary differential equations governing the modulation of theamplitudes and phases. Steady state solutions and their stabilityare computed for selected values of the system parameters. Theresults obtained by the two methods are in excellent agreement.Numerical solutions are carried out and graphical representationsof the results are presented and discussed
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