Mathematical modeling of vibration devices

P. A. Vel'misov ; A. V. Ankilov ; Yu. V. Pokladova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 37-49.

Résumé

Mathematical models of vibration devices designed to intensify technological processes are considered. Mathematical models are initial-boundary-value problems for coupled systems of partial differential equations for hydrodynamic functions and deformation functions of elastic elements. We examine the dynamics and dynamic stability of elastic elements. The study of dynamics is based of the Bubnov–Galerkin method. The study of dynamical stability is based on the construction of positive definite Lyapunov-type functionals.

Détail

Keywords: aerohydroelasticity, elastic plate, deformation, dynamics, stability, partial differential equation, Bubnov–Galerkin method, Lyapunov functional.

Bibliographie

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