Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Saratov Univ. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, Volume 18, Issue 4, Pages 397–411
DOI: https://doi.org/10.18500/1816-9791-2018-18-4-397-411
(Mi isu775)
 

This article is cited in 2 scientific papers (total in 2 papers)

Scientific Part
Mechanics

Approximate theory of a laminated anisotropic plate vibrations

A. K. Belyaeva, A. V. Zelinskayab, D. N. Ivanovb, N. F. Morozovb, N. V. Naumovab, P. E. Tovstikb, T. P. Tovstika

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 61 Bolshoj Pr., V. O., St. Petersburg 199178, Russia
b Saint Petersburg State University, 7–9 Universitetskaya Nab., St. Petersburg 199034, Russia
Full-text PDF (290 kB) Citations (2)
References:
Abstract: The multi-layered plate vibration is investigated. A two-dimensional asymptotic model of the second order accuracy with respect to the small thickness parameter is proposed with account for the transverse shear and the normal fibre extension. The model is appropriate for a monoclinic plate described by 13 elastic moduli which is heterogeneous in the thickness direction. In particular, the model can be applied to a multi-layered plate consisting of orthotropic layers of arbitrary orientation. In this case the elastic moduli are piece-wise constant functions. The elastic and inertia properties of plate are assumed to be constant in the tangential directions. The main achievement of this work is derivation of the equivalent constant coefficients of 2D system of partial differential equations of the second order accuracy. In the first approximation these coefficients can be found based on the Kirchhoff–Love hypotheses on the straight normal, while a more complex asymptotic algorithm is used for second approximation. For a multi-layered plate the influence of transverse shear with alternating hard and soft layers is discussed. More attention is given to a plate which is infinite in the tangential directions. The solution is shown to be essentially simplified since no boundary condition is needed and the solution can be expressed in terms of functions which are harmonic in the tangential directions. For this solution the error of 2D model is estimated by comparison with the numerical solution of the three-dimensional problem of elasticity theory, since for harmonic case it is reduced to one-dimensional equations in the thickness direction. Free and forced bending vibration and long-length bending wave propagation are investigated under harmonic approximation. In general case two different natural frequencies are shown to correspond to a fixed bending mode. The dependence of wave velocity on the wave propagation direction is found out.
Key words: anisotropic multi-layered plate, 2D model of the second order accuracy, bending vibrations and waves in a plate.
Funding agency Grant number
Russian Foundation for Basic Research 16-51-52025_МНТ_а
16-01-00580_a
This work was supported by the Russian Foundation for Basic Research (projects nos. 16.51.52025 MNT-a, 16.01.00580-a).
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: A. K. Belyaev, A. V. Zelinskaya, D. N. Ivanov, N. F. Morozov, N. V. Naumova, P. E. Tovstik, T. P. Tovstik, “Approximate theory of a laminated anisotropic plate vibrations”, Izv. Saratov Univ. Math. Mech. Inform., 18:4 (2018), 397–411
Citation in format AMSBIB
\Bibitem{BelZelIva18}
\by A.~K.~Belyaev, A.~V.~Zelinskaya, D.~N.~Ivanov, N.~F.~Morozov, N.~V.~Naumova, P.~E.~Tovstik, T.~P.~Tovstik
\paper Approximate theory of a laminated anisotropic plate
vibrations
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2018
\vol 18
\issue 4
\pages 397--411
\mathnet{http://mi.mathnet.ru/isu775}
\crossref{https://doi.org/10.18500/1816-9791-2018-18-4-397-411}
\elib{https://elibrary.ru/item.asp?id=36716504}
Linking options:
  • https://www.mathnet.ru/eng/isu775
  • https://www.mathnet.ru/eng/isu/v18/i4/p397
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
    Statistics & downloads:
    Abstract page:237
    Full-text PDF :93
    References:27
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024