Materials Science

, Volume 54, Issue 3, pp 368–377 | Cite as

Transverse Vibration of an Orthotropic Plate with a Collection of Holes of Arbitrary Configuration and Mixed Boundary Conditions

  • Т. V. ShopaEmail author

Within the framework of a refined theory that takes into account the transverse shear strains and the inertial components, we consider the problem of stationary vibration of an orthotropic bounded plate containing an arbitrary number of curvilinear holes. Mixed boundary conditions harmonic in time are analyzed both on the outer boundary of the plate and on the contours of the holes. The solution is constructed on the basis of the indirect boundary-element method. We use a sequential approach to the representation of Green functions. Integral equations are solved by the collocation method. We also present numerical results obtained for a rectangular plate with two circular holes.


vibration orthotropic plate holes indirect boundary element method 


  1. 1.
    S. S. Hota and P. Padhi, “Vibration of plates with arbitrary shapes of cutouts,” J. Sound Vibrat., 302, No. 4–5, 1030–1036 (2007).CrossRefGoogle Scholar
  2. 2.
    L. Kurpa, O. Mazur, and V. Tkachenko, “Dynamical stability and parametrical vibrations of laminated plates with complex shape,” Lat. Amer. J. Solids Struct., 10, 175–188 (2013).Google Scholar
  3. 3.
    T. Shopa, “Vibration of an orthotropic panel of double curvature with a set of holes of any configuration,” Visn. Ternopil. Nats. Tekh. Univ., No. 3, 63–74 (2012).Google Scholar
  4. 4.
    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
  5. 5.
    J. Lighthill, Introduction to Fourier Analysis and Generalized Functions, Cambridge Univ. Press, Cambridge (1958).CrossRefGoogle Scholar
  6. 6.
    M. A. Sukhorol’s’kyi, Functional Sequences and Series [in Ukrainian], Rastr-7, Lviv (2010).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

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

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