The optimal local loading regimes of a vibrating rod (one endpoint of the rod is fixed, while the second is stress-free), which ensure the damping of certain modes of elastic vibration over a minimal time interval, for a minimal norm of the control function and also under the simultaneous minimization of the time and the norm of the load function are given.
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Ya. I. Burak, Yu. D. Zozulyak, and B. V. Gera, Optimization of Transition Processes in Thermoelastic Shells [in Russian], Naukova Dumka, Kiev (1984).
A. G. Butkovskii, Methods for the Control of Systems with Distributed Parameters [in Russian], Nauka, Moscow (1975).
A. G. Butkovskii and L. M. Pustyl'nikov, Theory of Moving Control of Systems with Distributed Parameters [in Russian], Nauka, Moscow (1980).
L. H. Donnell, Beams, Plates, and Shells [Russian translation], Nauka, Moscow (1982).
V. Komkov, Optimal Control of Vibration Damping of Simple Elastic Systems [in Russian], Mir, Moscow (1975).
Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 71–75, 1987.
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Gera, B.V. Control of damped vibrations of a rod by means of a concentrated force or moment loading. J Math Sci 65, 1986–1990 (1993). https://doi.org/10.1007/BF01097486
- Control Function
- Minimal Time
- Minimal Norm
- Concentrate Force