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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Thermal impact produced onto a thermoelastic plate that demonstrates special boundary conditions

Vestnik MGSU 9/2012
  • Egorychev Oleg Aleksandrovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Egorychev Oleg Olegovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor 8 (495) 287-49-14, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Fedosova Anastasia Nikolaeva - Moscow State University of Civil Engineering (MSUCE) Senior Lecturer, Department of Higher Mathematics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 109 - 115

The problem of forced vibrations of plates exposed to the thermal impact is interesting both
as a theoretical implication and an issue of practical importance. A thermal impact causes formation
of a non-steady temperature field. Thereafter, some materials turn fragile and cannot withstand the
exposure to the impact of a thermal field.
The authors propose a solution to the problem of influence of a thermal impact onto an isotropic
plate that demonstrates special boundary conditions, if its two opposite edges are simply
supported, and the surface temperature is equal to zero, while the two other edges might have an
arbitrary type of fixation and an arbitrary thermal mode.
In the first part of the paper, the authors provide their derivation of the elastic plate vibration
equation, if the plate is exposed to the thermal impact under the pre-set boundary conditions.
In the second part of the paper, the authors provide their solution to the aforementioned problem
based on a strictly mathematical approach. Their solution is presented as an integral function
of the plate deflection. The solution in question may be reduced to algebraic frequency equations
by using the method of expansion of trigonometric functions. Thus, it is possible to identify natural
frequencies of the plate vibration caused by the thermal impact.

DOI: 10.22227/1997-0935.2012.9.109 - 115

References
  1. Abo-el-nour N., Abd-alla, Nadia A. Askar. The Numerical Computation for Anti-symmetric Modes of Vibration of a Transversely Isotropic Generalized Thermoelastic Plate. International Journal of Mathematical Archive. 2012, no. 3(3), pp. 1091—1101.
  2. Hetnarski Richard B., Eslami M. Reza. Thermal Stresses – Advanced Theory and Applications. Series: Solid Mechanics and Its Applications. Springer Science + Business Media, 2009, vol. 158.
  3. Beknazarov M.N., Blazhevich S.V., Nemtsev S.N. K voprosu o termouprugikh kolebaniyakh tonkoy ellipticheskoy plastinki, vozbuzhdaemykh impul’snym puchkom zaryazhennykh chastits [Concerning Thermal Elastic Vibrations of a Thin Elliptical Plate Caused by a Pulsed Beam of Charged Particles]. Vzaimodeystvie zaryazhennykh chastits s kristallami [Interaction of Charged Particles with Crystals]. Proceedings of the 38th International Conference. 2007, Moscow, May 29-31, pp. 27—28.
  4. Bondarenko N.S. Termouprugoe sostoyanie transversal’no-izotropnykh plastin pri sosredotochennykh teplovykh vozdeystviyakh [Thermoelastic State of Transversely Isotropic Plates Exposed to Concentrated Thermal Effects]. Donetsk National University, Donetsk, 2010, 169 p.
  5. Filippov I. G., Cheban V. G. Matematicheskaya teoriya kolebaniy uprugikh i vyazkouprugikh plastin i sterzhney [Mathematical Theory of Vibrations of Elastic and Viscoelastic Plates and Rods]. Kishinev, Shtiintsa Publ., 1988.
  6. Podstrigach Ya.S., Kolyano Yu.M. Obobshchennaya termomekhanika [Generalized Thermal Mechanics]. Kiev, Naukova Dumka Publ., 1976.
  7. Egorychev O.O. Issledovaniya kolebaniy ploskikh elementov konstruktsiy [Research of Vibrations of Flat Elements of Structures]. Ìoscow, Arkhitektura-S Publ., 2009.
  8. Bogdanov A.V., Poddaeva O.I. Sobstvennye kolebaniya uprugoy trekhsloynoy plastiny, dva protivopolozhnykh kraya kotoroy sharnirno zakrepleny, a dva drugikh svobodny ot zakrepleniya [Natural Vibrations of an Elastic Three-layer Plate, If Its Two Opposite Edges are Pinned, While the Other Two Are Not Fixed]. Teoriya i praktika rascheta zdaniy, sooruzheniy i elementov konstruktsiy. Analiticheskie i chislennye metody [Theory and Practice of Analysis of Buildings, Structures and Structural Elements. Analytical and Numerical Methods]. Proceedings of the 3rd International Scientific Conference, Moscow, 2010, pp. 81—87.
  9. Bogdanov A.V., Poddaeva O.I. Vyvod chastotnogo uravneniya sobstvennykh kolebaniy uprugoy trekhsloynoy plastiny, dva protivopolozhnykh kraya kotoroy sharnirno zakrepleny, a dva drugikh zhestko zakrepleny (analiticheskiy metod resheniya) [Derivation of the Frequency Equation of Natural Vibrations of an Elastic Three-layer Plate, If Its Two Opposite Edges Are Pinned, While the Other Two Edges Are Rigidly Fixed (an Analytical Solution). Teoriya i praktika rascheta zdanii, sooruzhenii i elementov konstruktsii. Analiticheskie i chislennye metody [Theory and Practice of Analysis of Buildings, Structures and Structural Elements. Analytical and Numerical Methods]. Proceedings of the 2nd International Scientific Conference, Moscow, 2009, pp. 65—69.

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