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Subharmonic Vibrations and Chaos in Forced Nonlinear Oscillators
Author(s) -
Schmidt G.,
Seisl M.
Publication year - 1993
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19930730209
Subject(s) - subharmonic , vibration , chaotic , amplitude , nonlinear system , harmonic , mathematics , chaos (operating system) , continuation , period doubling bifurcation , physics , subharmonic function , mathematical analysis , control theory (sociology) , acoustics , computer science , quantum mechanics , bifurcation , computer security , artificial intelligence , control (management) , programming language
For forced nonlinear oscillators, different subharmonic vibrations are investigated analytically by higher approximations, checked by computer algebra, and numerically by a damped Newton procedure combined with a continuation algorithm (BIFPACK package by R. Seydel). Especially for a damping value which leads to a frequency region with chaotic behaviour, second subharmonic vibrations appear with amplitudes of the same size as for the harmonic vibrations, whereas third subharmonic vibrations appear only for lower frequencies. This gives an explaination for the existence of second and later on of third subharmonic periodic windows in the period doubling route to chaos.