Premium
To the Analysis of Autoparametric Systems
Author(s) -
Tondl A.
Publication year - 1997
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.19970770603
Subject(s) - nonlinear system , parametric statistics , parametric oscillator , excitation , resonance (particle physics) , degrees of freedom (physics and chemistry) , vibration , saturation (graph theory) , physics , mathematics , mathematical analysis , classical mechanics , quantum mechanics , statistics , combinatorics
Autoparametric systems represent a special class of nonlinear systems. Such a system has at least two parts, i.e. two degrees of freedom at least. The first part — the oscillator — vibrates due to external or parametric excitations or due to self‐excitation. A typical feature is represented by the existence of the semi‐trivial solution, which means that only the oscillator vibrates. Under certain conditions the semi‐trivial solution is unstable, and autoparametric resonance is induced. Several examples of these systems together with a survey of the investigation results are presented. Typical properties like saturation effect and the occurrence of non‐periodic vibration are illustrated on examples.