EFFICIENT DETERMINATION OF HIGHER-ORDER PERIODIC-SOLUTIONS USING N-MODE HARMONIC-BALANCE

Citation
P. Donescu et Ln. Virgin, EFFICIENT DETERMINATION OF HIGHER-ORDER PERIODIC-SOLUTIONS USING N-MODE HARMONIC-BALANCE, IMA journal of applied mathematics, 56(1), 1996, pp. 21-32
Citations number
15
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
02724960
Volume
56
Issue
1
Year of publication
1996
Pages
21 - 32
Database
ISI
SICI code
0272-4960(1996)56:1<21:EDOHPU>2.0.ZU;2-D
Abstract
This paper presents a systematic procedure to explicitly determine the algebraic equations arising from the method of harmonic balance with an arbitrary number of modes in the assumed solutions. The technique c an be used for a wide variety of nonlinear oscillators (including syst ems of ordinary differential equations). The method is illustrated in the case of second-order differential equations with nonlinear restori ng force. Although numerical methods have been employed to solve the r esulting systems of algebraic equations, the general approach is analy tic. As such, this study confirms independently (i.e. nonsimulation) t he period-doubling cascade of an escape equation including the bifurca tion universal scaling laws.