DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Self-excited oscillations of a transversely isotropic plate, one edge of which is rigidly fixed and the other three edges are hinged, if the plate rests on thestrain foundation

Vestnik MGSU 7/2013
  • Egorychev Oleg Aleksandrovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Professor, Department of Theoretical Mechanics and Aerodynamics; +7 (499) 183-24-01, 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 .
  • Stepanov Roman Nikolaevich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Theoretical Mechanics and Aerodynamics; +7 (499) 183-24-01, 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 .
  • Zapol’nova Evgeniya Valer’evna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Theoretical Mechanics and Aerodynamics, 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 27-32

Today, an enormous number of research papers by foreign and domestic authors cover the research into vibration of plates. Despite this variety, oscillation of transversely isotropic plates remains understudied. The most substantial contribution into this area of research was made by S.A. Ambartsumyan, V.V. Bolotin, E.J. Brunelle, and M. Levinson. The author provides the summary of a frequency equation describing self-excited oscillations of a transversely isotropic plate resting on the strain foundation, if one edge of the plate is rigidly fixed and the other three edges are hinged. The problem was solved using the approximate method employed to derive the frequency equation needed to identify self-excited oscillations of the plate. The formulas, derived by the author and designated for the identification of frequencies of free transverse vibrations of the plate, are suitable for practical application; they may be applied for the identification of the nature of dependence between natural frequencies of the plate and its geometry.

DOI: 10.22227/1997-0935.2013.7.27-32

References
  1. Ambartsumyan S.A. Obshchaya teoriya anizotropnykh obolochek [General Theory of Anisotropic Shells]. Moscow, Nauka Publ., 1974, 446 p.
  2. Bolotin V.V. Sovremennye napravleniya v oblasti dinamiki plastin i obolochek. Kn. Teoriya plastin i obolochek [Modern Trends in Dynamics of Plates and Shells. In: Theory of Plates and Shells]. Kiev, Naukova Dumka Publ., 1962, pp. 16—32.
  3. Brunelle E.J. Buckling of Transversely Isotropic Mindlin Plates. AIAA Journal. 1971, 9, no. 6, pp. 1018—1022.
  4. Levinson M. Free Vibrations of a Simply Supported, Rectangular Plate: an Exact Elasticity Solution. Journal of Sound and Vibration. 22 January, 1985, no. 2, pp. 289—298.
  5. Egorychev O.A., Egorychev O.O., Zapol’nova E.V. Sobstvennye kolebaniya transversal’no-izotropnoy plastiny, lezhashchey na deformiruemom osnovanii, odin kray kotoroy uprugo zakreplen, a tri drugikh sharnirno operty [Self-excited Oscillations of a Transversely 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 [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 11, pp. 45—55.
  6. 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. 190 ð.
  7. Egorychev O.O. Kolebaniya ploskikh elementov konstruktsiy [Vibrations of Flat Elements of Structures]. Moscow, ASV Publ., 2005, 239 p.

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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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