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Materials Science

, Volume 55, Issue 1, pp 94–104 | Cite as

Transverse Vibrations of an Orthotropic Plate with a Collection of Inclusions of Any Configuration with Different Types of Connections with the Matrix

  • T. V. ShopaEmail author
Article
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Within the framework of an improved theory that takes into account transverse shear strains and inertial components, we construct the solution of the problem of stationary flexural vibration of an orthotropic plate containing a collection of arbitrarily located curvilinear inclusions. We analyze various types of connections of these inclusions with the plate. The outer boundary of the plate has an arbitrary geometric configuration. In this boundary, we impose mixed boundary conditions harmonic in time. The solution is constructed by using the indirect method of boundary element. We used the sequential approach to the representation of Green functions.

Keywords

vibration orthotropic plate holes indirect method of boundary elements 

References

  1. 1.
    M. Sukhorolsky and T. Shopa, “The vibration of rectangular orthotropic plate with massive inclusions,” Comp. Assist. Mech. Eng. Sci.,15, 369–376 (2008).Google Scholar
  2. 2.
    U. Babuscu Yesil, “Forced vibration analysis of prestretched plates with twin circular inclusions,” J. Eng. Mech.,141, No. 1, 04014099-1-04014099-16 (2014).Google Scholar
  3. 3.
    T. Shopa, “Vibration of an orthotropic panel of double curvature with a collection of inclusions of any configuration and elastic interlayers,” Visn. Ternopil. Derzh. Tekh. Univ., No. 1, 71–84 (2013).Google Scholar
  4. 4.
    T. V. Shopa, “Vibration of an orthotropic plate with a collection of inclusions of any configuration,” in: Abstr. of the Conf. of Young Scientists “Pidstryhach Readings–2016” [in Ukrainian], Lviv (2016).Google Scholar
  5. 5.
    T. V. Shopa, “Transverse vibration of an orthotropic plate with a collection of holes of arbitrary configuration and mixed boundary conditions,” Fiz.-Khim. Mekh. Mater.,54, No. 3, 73–80 (2018); English translation:Mater. Sci.,54, No. 3, 368–377 (2018).CrossRefGoogle Scholar
  6. 6.
    Ya. I. Burak, Yu. K. Rudavs’kyi, and M. A. Sukhorol’s’kyi, Analytic Mechanics of Locally Loaded Shells [in Ukrainian], Intelekt-Zakhid, Lviv (2007).Google Scholar
  7. 7.
    J. Lighthill, Introduction to Fourier Analysis and Generalized Functions, Cambridge Univ. Press, Cambridge (1958).CrossRefGoogle Scholar
  8. 8.
    M. A. Sukhorol’s’kyi, Functional Sequences and Series [in Ukrainian], Rastr-7, Lviv (2010).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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