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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

SELF-EXCITED OSCILLATIONS OF A TRANSVERSALLY ISOTROPIC PLATE RESTING ON THE STRAINED FOUNDATION BED, IF ONE OF THE PLATE EDGES IS FLEXIBLY FIXED, WHILE THE THREE OTHER EDGES ARE HINGED

Vestnik MGSU 11/2012
  • Egorychev Oleg Aleksandrovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Professor, Department of Theoretical Mechanics and Thermodynamics, +8 (495) 739-33-63, Moscow State University of Civil Engineering (MGSU), 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 (MGSU) Doctor of Technical Sciences, Professor, Professor, Chair, Department of Theoretical Mechanics and Thermodynamics, First Vice-Chancellor, +8 (495) 739-33-63, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zapolnova Evgeniya Valerevna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Theoretical Mechanics and Thermodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 55 - 60

Plates are widely used as flat structural elements in various spheres of construction and engineering.
Development of industrial and residential building techniques furthers development of
the construction science. Therefore, the design and the refined theory of plate vibrations is one
of signifi cant issues considered within the framework of the applied theory of elasticity, which is of
practical interest to the researchers. The authors provide a summary of frequency equations that
describe self-excited oscillations of a transversally isotropic plate resting on the strain foundation
bed, if one edge of the plate is flexibly fixed and the other three edges are hinged. Oscillations are
described by partial differential equations of the fourth order. The problem is resolved through the
employment of an approximate method of decompositions. As a result, the frequency equation is
derived to identify self-excited lateral oscillations of the plate. The equations derived by the authors
for the purpose of identifi cation of the frequencies of self-excited transverse vibrations of a plate are
fit for practical use, and they may be applied in calculations to identify the dependence of the selfexcited
frequency of the plate on its geometry.

DOI: 10.22227/1997-0935.2012.11.55 - 60

References
  1. Egorychev O.O. Kolebaniya ploskikh elementov konstruktsiy [Vibrations of Flat Elements of Structures]. Moscow, ASV Publ., 2005, 239 p.
  2. Egorychev O.A., Egorychev O.O. Uravnenie kolebaniy predvaritel’no napryazhennykh transversal’no-izotropnykh plastin [Equation of Vibrations of Pre-stressed Transversally Isotropic Plates]. Vestnik otdeleniya stroitel’nykh nauk [Bulletin of Section of Construction Sciences]. 2009, no. 13, p. 9.
  3. Egorychev O.A., Egorychev O.O., Poddaeva O.I., Prokhorova T.V. Sobstvennye kolebaniya uprugoy plastinki, lezhashchey vnutri deformiruemoy sredy, dva protivopolozhnykh kraya kotoroy uprugo zakrepleny, a dva drugikh sharnirno operty [Natural Vibrations of a Flexible Plate in a Strain Media, If the Two Opposite Edges Are Flexibly fi xed, and the Two Other Edges are Hinged]. Internet-vestnik VolgGASU. Ser.: Politematicheskaya [Internet-Vestnik VolgGASU. Multidisciplinary Series]. 2011, no. 3(17), 9 p. Available at: www.vestnik.vgasu.ru.
  4. Egorychev O.A., Egorychev O.O., Poddaeva O.I. Priblizhennye uravneniya poperechnykh kolebaniy ploskikh elementov stroitel’nykh konstruktsiy [Approximated Equations of Transverse Vibrations of Flat Elements of Structures]. Moscow, MGSU Publ., 2008, 164 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.

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