Forced Oscillations and Convex Superposition in Piecewise-Linear Systems

Several aspects of the theory of forced oscillations of piecewise-linear systems are considered. First of all, the general probelm of determining such periodic solutions is formulated and the principal methods of solving the problem are described briefly. By way of illustration, forced periodic solu...

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Bibliographic Details
Published inSIAM review Vol. 7; no. 2; pp. 205 - 222
Main Author Fleishman, B. A.
Format Journal Article
LanguageEnglish
Published Philadelphia The Society for Industrial and Applied Mathematics 01.04.1965
Society for Industrial and Applied Mathematics
Subjects
Coefficients
Control systems
Differential equations
Forced vibration
Fourier series
Mathematical functions
Scalars
Sine function
Vibration
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Summary:Several aspects of the theory of forced oscillations of piecewise-linear systems are considered. First of all, the general probelm of determining such periodic solutions is formulated and the principal methods of solving the problem are described briefly. By way of illustration, forced periodic solutions of the simplest kind are determined for a second-order on-off system subject to a sinusoidal external force. Next, piecewise-linear systems are shown to possess a property of convex superposition with respect to any set of responses (to different excitations) which are "synchronous", i.e., are in phase as they switch from one linear branch of the piecewise-linear function to another. Finally, for sets of periodic responses which are "almost synchronous", a conjecture is offered concerning "approximate" superposition; in this connection the example involving the second-order system is reconsidered.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1445
1095-7200
DOI:10.1137/1007037