Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
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IssuesArchive of Issues2002-6pp.18-28

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Total articles in the database: 9145
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K. S. Matviichuk, "Engineering stability analysis of controlled elastic flying systems," Mech. Solids. 37 (6), 18-28 (2002)
Year 2002 Volume 37 Number 6 Pages 18-28
Title Engineering stability analysis of controlled elastic flying systems
Author(s) K. S. Matviichuk (Kiev)
Abstract The paper deals with the engineering stability analysis [1-14] of dynamic states of elongated rocket-type elastic flying vehicles during the longitudinal vertical motion. Such flying vehicles have a shape of thin elongated bodies with variable cross section and undergo large transverse deformations and vibrations during the flight. As the dimensions of such systems increase, their relative rigidity decreases, which makes the influence of various vibrations (including elastic vibrations) on the flight and flight control substantial. The interaction of the deformation with angular motions of the system's body, external aerodynamic forces, and internal hydrodynamic disturbances due to vibrating liquid in the vehicle tanks can lead to such undesired phenomena as self-sustained vibrations or buckling. As a result, the system can fail to flight along the prescribed trajectory. To resist deviations from the prescribed angular and other motions, the vehicle is equipped with a control system. If the control law is chosen improperly, the control system may excite the motion of the liquid in the tanks and elastic vibrations. For the control law considered in the present paper, we have obtained sufficient conditions for the engineering stability of the dynamical system under consideration on both finite and infinite time intervals. For the stability analysis, we investigated a comparison method based on the optimization of distributed processes combined with Lyapunov's direct method. The investigations of the present paper are based on the results of [15-26].
1.  K. A. Abgaryan, "Stability of motion on a finite interval," in Achievements in Science and Technology. General Mechanics. Volume 3 [in Russian], pp. 43-124, VINITI, Moscow, 1976.
2.  F. D. Bairamov, "On the engineering stability of distributed systems subject to constant disturbances," Izv. Vuzov. Aviatsionnaya Tekhnika, No. 2, pp. 5-11, 1974.
3.  F. D. Bairamov, "Providing the engineering stability for controlled systems," in Problems of Analytical Mechanics, Stability, and Control of Motion [in Russian], pp. 134-139, Nauka, Novosibirsk, 1991.
4.  B. N. Bublik, F. G. Gerashchenko, and N. F. Kirichenko, Structural-parametric Optimization and Stability of Beam Dynamics [in Russian], Naukova Dumka, Kiev, 1985.
5.  F. G. Gerashchenko and N. F. Kirichenko, "Analysis of problems of practical stability and stabilization of motion," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 15-24, 1975.
6.  V. M. Kuntsevich and M. M. Lychak, Synthesis of Automatic Control Systems Using Lyapunov Functions [in Russian], Nauka, Moscow, 1977.
7.  T. K. Sirazetdinov, Stability of Distributed Systems [in Russian], Nauka, Novosibirsk, 1987.
8.  K. S. Matviichuk, "On the comparison method for nearly-hyperbolic differential equations," Differentsial'nye Uravneniya [Differential Equations], Vol. 20, No. 11, pp. 2009-2011, 1984.
9.  K. S. Matviichuk, "Engineering stability of distributed processes subject to parametric excitation," PMM [Applied Mathematics and Mechanics], Vol. 50, No. 2, pp. 210-218, 1986.
10.  K. S. Matviichuk, "On the engineering stability of a panel in a gas flow," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 6, pp. 93-99, 1988.
11.  K. S. Matviichuk, "Engineering stability theory for parametrically excited panels in a gas flow," Izv. AN SSSR. MTT. No. 4, pp. 122-131, 1990.
12.  K. S. Matviichuk, "On the engineering stability conditions for solutions of a nonlinear boundary-value problem governing the dynamic behavior in a supersonic gas flow," Prikladnaya Mekhanika, Vol. 34, No. 4, pp. 101-106, 1990.
13.  K. S. Matviichuk, "Engineering stability conditions for distributed controlled processes," Problemy Upravleniya i Informatiki, No. 2, pp. 84-93, 1998.
14.  K. S. Matviichuk, "On the engineering stability conditions for a nonlinear boundary-value problem characterizing processes subject to parametric excitations in Hilbert space," Ukrainskii Matem. Zh., Vol. 51, No. 3, pp. 349-363, 1999.
15.  A. M. Letov, Mathematical Theory of Control Processes [in Russian], Nauka, Moscow, 1981.
16.  T. K. Sirazetdinov, "On the optimal control of elastic flying vehicles," Avtomatika i Telemekhanika, No. 7, pp. 5-19, 1966.
17.  T. K. Sirazetdinov, "On the synthesis of the optimal control for elastic flying vehicles," Izv. Vuzov. Aviatsionnaya Tekhnika, No. 4, pp. 30-40, 1967.
18.  T. K. Sirazetdinov, Optimization of Distributed Systems [in Russian], Nauka, Moscow, 1977.
19.  K. A. Lur'e, Optimal Control in Mathematical Physics [in Russian], Nauka, Moscow, 1975.
20.  H. W. Liepmann and A. Roshko, Fundamentals of Gas Dynamics [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1960.
21.  G. G. Chernyi, Gas Flow with High Supersonic Velocity, Fizmatgiz, Moscow, 1959.
22.  K. S. Kolesnikov, Liquid-propellant Rocket as an Object of Control [in Russian], Mashinostroenie, Moscow, 1969.
23.  V. V. Rumyantsev, "On the theory of motion of rigid bodies with cavities filled with a fluid," PMM [Applied Mathematics and Mechanics], Vol. 30, No. 1, pp. 51-66, 1966.
24.  Yu. A. Mitropol'skii, Method of Averaging in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev, 1971.
25.  V. M. Matrosov, L. Yu. Anapol'skii, and S. N. Vasil'ev, Comparison Method in Mathematical Theory of Systems [in Russian], Nauka, Novosibirsk, 1980.
26.  J. Szarski, Differential Inequalities, PWN, Warshawa, 1967.
Received 13 March 2000
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