Dynamic stability of elastic plate at jet flow
A. V. Ankilov1, P. A. Velmisov2
|Annotation||The mathematical model of the dynamic system containing an elastic plate at a one-sided flow of stream of ideal incompressible gas with a separation of jet according to Kirchhoff's scheme is offered. The behavior of elastic material is described by the nonlinear model considering both longitudinal, and transversal deformations of an elastic plate. The solution of an aerohydrodynamic part of a problem based on methods of the theory of functions of complex variable is given. The related system of the integro-differential equations with private derivatives containing only unknown plate deformations functions is received. On the basis of building of the functional corresponding to this system of the equations the sufficient stability conditions of solutions of system are received. Definition of stability of an elastic body corresponds to the Lyapunov's concept of stability of dynamic systems.|
|Keywords||aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, subsonic flow of gas, the differential equations in private derivatives, functional|
1Andrey V. Ankilov, Associate Professor, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venetc Str., Ulyanovsk 432027, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-5946-8535, firstname.lastname@example.org
2Petr A. Velmisov, Head of Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venetc Str., Ulyanovsk 432027, Russia), Dr. Sci. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-7825-7015, email@example.com.
Citation: A. V. Ankilov, P. A. Velmisov, "[Dynamic stability of elastic plate at jet flow]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 116–129 (In Russian)