International Scientific Journal

Authors of this Paper

External Links


In this paper, the problem of thermally induced vibration suppression in a thermoelastic beam is studied. Physical equivalent of the present problem is that a thermoelastic beam is suddenly entering into daylight zone and vibrations are induced due to heating on the upper surface of the beam or thermoelastic beam in a spacecraft enters to intensive sunlight area just after leaving a shadow of a planet. Thermally induced vibrations are suppressed by means of minimum using of control forces to be applied to dynamic space actuators. Objective functional of the problem is chosen as a modified quadratical functional of the kinetic energy of the thermoelastic beam. Necessary optimality condition to be satisfied by an optimal control force is derived in the form of maximum principle, which converts the optimal vibration suppression problem to solving a system of distributed parameters system linked by initial-boundary-terminal conditions. Solution of the system is achieved via MATLAB© and simulated results reveal that thermally induced vibration suppression by means of dynamic space actuators are very effective and robust.
PAPER REVISED: 2021-02-17
PAPER ACCEPTED: 2021-03-10
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2017 - 2024]
  1. Yu, Y. Y., Thermally Induced Vibration and Flutter of a Flexible Boom, Journal Spacecraft, 6 (1969), 8, pp. 901-908
  2. Boley, B. A., Approximate Analysis of Thermally Induced Vibrations of Beams and Plates, Journal Applied Mechanics, 39 (1972), 1, pp. 212-216
  3. Manolis, G. D., Thermally Induced Vibrations of Beam Structures, Computer Methods and Applied Mechanics and Engineering, 21 (1980), 3, pp. 337-355
  4. Zener, C., Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction, Physical Review, 53 (1938), 1, pp. 90-99
  5. Kinra, V. K., Milligan, K. B., A Second Law Analysis of Thermoelastic Dampings, Journal of Applied Mechanics, 61 (1994), 1, pp. 71-76
  6. Kidawa-Kukla, J., Vibration of a Beam Induced by Harmonic Motion of a Heat Source, Journal of Sound and Vibration, 205 (1997), 2, pp. 213-222
  7. Kucuk, I., et. al., Optimal Control of a Beam with Kelvin-Voigt Damping Subject to Forced Vibrations Using a Piezoelectric Patch Actuator, Journal of Vibration and Control, 21 (2015), 4, pp. 701-713
  8. Jayasuriya, S., Choura, S., Active Quenching of a Set of Predetermined Vibratory Modes of a Beam by a Single Fixed Actuator, Int. Journal of Control, 51 (1990), 2, pp. 445-467
  9. Choura, S., et. al., On the Modelling and Open Loop Control of a Rotating Thin Flexible Beam, ASME J. Dynamic systems, Measurement Control, 113, Mar., pp. 26-33
  10. Jayasuriya, S., Choura, S., On the Finite Settling Time and Residual Vibration Control of Flexible Structures, Journal Sound Vibration, 148 (1991), 1, pp. 117-136
  11. Goktepe Korpeoglu, S., Optimal Vibration Control of an Isotropic Beam through Boundary Conditions, Thermal Science, 25 (2021), Special Issue 1, pp. S111-S120
  12. Kucuk, I., et. al., Optimal Piezoelectric Control of a Plate Subject to Time-Dependent Boundary Moment and Forcing Function for Vibration Damping, Computers and Mathematics with Applications, 69 (2015), 4, pp. 291-303
  13. Choura, S., Jayasuriya, S., Control of Distributed Parameter Systems by Moving Force Actuators, Journal Guidance, Control, Dynamics, 14 (1991), 6, pp. 1200-1207
  14. Lagnese, J. E., The Reachability Problem for Thermoelastic Plates, Arch. Rational Mech. Analysis, 112 (1990), Sept., pp. 223-267
  15. Pamuk, M. T., Numerical Study of Natural Convection in an Enclosure with Discrete Heat Sources on One of Its Vertical Walls, Thermal Science, 25 (2021), 1A, pp. 267-277
  16. Edberg, D. L., Control of Flexible Structures by Applied Thermal Gradients, AIAA J., 25 (1987), 6, pp. 877-883
  17. Boley, B. A., Weiner, J. H., Theory of Thermal Stress, John Wiley and Sons, New York, USA, 1960
  18. Boley, B. A., Thermally Induced Vibrations of Beams, Journal Aeronaut Sci., 23 (1956), pp. 179-181
  19. Kukla, J. K., Application of the Green Functions to the Problem of the Thermally Induced Vibration of a Beam, Journal of Sound and Vibration, 262 (2003), 4, pp. 865-876
  20. Pedersen, M., Functional Analysis in Applied Mathematics and Engineering, CRC Press, Boca Raton, Fla., USA, 2018
  21. Zachmaonoglou, E. C., Thoe, D. W., Intoduction to Partial Differential Equations with Applications, Dover Publ., New York, USA, 1986
  22. Guliyev, H. F., Jabbarova, K. S., The Exact Controllability Problem for the Second Order Linear Hyperbolic Equation, Differential Equations and Control Processes, 3 (2010)

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence