ON ONE PROBLEM OF OPTIMAL CONTROL OF VIBRATIONS OF A PLATE-STRIP IN A TEMPERATURE FIELD

Authors

DOI:

https://doi.org/10.46991/PYSU:A/2023.57.3.079

Keywords:

vibrations, thermal conductivity, optimal control, thermoelasticity

Abstract

The problem of optimal control of elastic vibrations of an isotropic plate-strip under the influence of temperature and force fields is studied. The function of changing the external load on the plane of the plate is represented as a control function. Optimal control is also carried out by the distribution function of the temperature of the external field over the plate. The well-known classical hypotheses of thermo-elastic bending of the plate are accepted. The equations of transverse vibrations of the plate and heat conduction in the plate are solved under the boundary conditions of heat transfer and the stress state on the planes of the plate. The method of Fourier series, the method of representing moment relations, the well-known method of minimizing the functional are used.

References

Butkovski A.G. Methods of Control of Systems with Distributed Parameters. Moscow, Nauka (1972), 332 (in Russian).

Jilavyan S.H., Grigoryan E.R., Khurshudyan As.Zh. Heating Control of Finite Rod with a Mobile Source. Archive of Control Sciences. Polish Academy of Sciences 31 (2021), 417-430. https://doi.org/10.24425/acs.2021.137425

Xu B., Lu X., Bai Y. A Spatiotemporal Fuzzy Control Approach for Complex Distributed Parameter System with Application to Thermal Processes. J. Process Control 127 (2023). https://doi.org/10.1016/j.jprocont.2023.102993

Wang Y.Z., Liu D., et al. Asymptotic Analysis of Thermoelastic Response in Functionally Graded Thin Plate Subjected to a Transient Thermal Shock. Compos. Struct. 139 (2016), 233-242. https://doi.org/10.1016/j.compstruct.2015.12.014

Ignaczak J. A Review: Thermoelasticity by Witold Nowackiy (2nd ed.). Oxford, Pergamon Press (1986).

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Published

2023-12-07

How to Cite

Grigoryan, E. R. (2023). ON ONE PROBLEM OF OPTIMAL CONTROL OF VIBRATIONS OF A PLATE-STRIP IN A TEMPERATURE FIELD. Proceedings of the YSU A: Physical and Mathematical Sciences, 57(3 (262), 79–85. https://doi.org/10.46991/PYSU:A/2023.57.3.079

Issue

Section

Mechanics