Engineering Transactions, 48, 2, pp. 99–118, 2000

Charitonov Theorem And Stability of Parametrically Excited Systems

A. Foryś
Cracow University of Technology
Poland

J. Kowynia
University of Mining And Metallurgy
Poland

The present paper concerns the application of the Charitonov theorem to an analysis of stability of parametrically excited mechanical or physical systems with intervally changing parameters of systems. In such systems the problems of stable solutions of the equation of motion also arise. In some methods the stability analysis of the parametrically excited systems with intervally changing parameters transformes into the analysis of stability of some $n$-th degree interval polynomials. On the basis of ChT we can check that the solution is stable in the whole interval of changing parameters, without constructing of the boundary of instability regions. Examples of application of the ChT to the analysis of stability of some special systems in steady states of the periodic parametric resonance are considered.
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