 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| B.F. Bairamov and F.D. Bairamov, "On Stability of a Class of Linear Systems with Distributed and Lumped Parameters," Mech. Solids. 54 (2), 245-250 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
2 |
Pages |
245-250 |
| DOI |
10.3103/S002565441903004X |
| Title |
On Stability of a Class of Linear Systems with Distributed and Lumped Parameters |
| Author(s) |
B.F. Bairamov (Naberezhnye Chelny Institute, Kazan Federal University, Naberezhnye Chelny, 423806 Russia, bbairamov@gmail.com)
F.D. Bairamov (Naberezhnye Chelny Institute, Kazan Federal University, Naberezhnye Chelny, 423806 Russia, fbairamovd@gmail.com) |
| Abstract |
The method of Lyapunov functions is used to investigate the stability of systems with distributed and lumped parameters, described by linear partial and ordinary differential equations. The
original high-order partial differential equations are represented by a first-order system of partial differential evolution equations and constraint equations; to do that, we introduce additional variables.
Passing to the first-order system of partial differential equations and representing ordinary differential
equations in the normal Cauchy form, we obtain a possibility to construct the Lyapunov function as a
sum of integral and classical quadratic forms and develop general methods of the investigation of the
stability of a broad class of systems with distributed and lumped parameters. For example, we consider
the stability of the work of the wind-driven lift pump and take into account the elasticity of the shaft
transmitting the torque from the wind engine to the pump. |
| Keywords |
systems with distributed and lumped parameters, stability, method of Lyapunov functions, quadratic forms |
| Received |
31 March 2017 |
| Link to Fulltext |
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