Ivan V. Kazachkov



The Theory and Applications of Parametric Excitation and Suppression of Oscillations in Continua: State of the Art

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The results by development of physical, mathematical and numerical models for parametric excitation and suppression of oscillations on the interfaces separating continuous media, for carrying out computing, physical and natural experiments by revealing the new phenomena and parametric effects, and for their use in improvement the existing and creation the perspective highly efficient technological processes are presented. Scientific novelty of this work consists in development of the theory and applications of parametric excitation and suppression of oscillations on the boundaries of continua on the samples of three tasks’ classes: flat and radial spreading film flows of viscous incompressible liquids, conductive as well as non-conductive ones; surfaces of phase transition from a liquid state into a solid one; and heterogeneous granular media. The external actions considered are: alternating electromagnetic, vibration, acoustic and thermal fields. Along with linear the non-linear parametric oscillations are investigated (including strongly non-linear) too and the results of theoretical studies are confirmed and supplemented with the corresponding experimental data. The general and specific peculiarities of parametrically excited oscillations and the new parametric effects revealed are discussed for technical and technological applications. First the general statement and substantiation of the problems studied is considered, and then the various parametric oscillations in continua are analyzed from common methodological base. Also the assessment of a current state of the problems, analysis of their features, prospects of further development and the main difficulties of the methodological, mathematical and applied character are presented.



Parametric, Wave, Excitation, Suppression, Instability, Stabilization, Control, Jet and Film Flow, Solidification Fronts, Interfaces of Continua




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Cite this paper

Ivan V. Kazachkov. (2017) The Theory and Applications of Parametric Excitation and Suppression of Oscillations in Continua: State of the Art. International Journal of Mathematical and Computational Methods, 2, 182-206


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