Exact analytical solution for a pie-shaped wedge thick plate under oscillating load

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A finite elastic wedge-shaped thick plate is considered. One of the faces is based on a rigid base, and the other is exposed to a dynamic oscillating load through an absolutely rigid overlay. On the side faces, conditions of sliding contact are fulfilled; at its end, the stresses are given. The solution is based on a special
linear transformation of Lamé’s equations and application of the vector integral transformations method. The proposed approach leads to a one-dimensional vector boundary value problem for which an exact solution is constructed. The analysis of the eigenfrequency value distribution and an estimation of the edge resonance frequency are done. An analogous problem is solved for the case when at the lower wedge plate’s face the sliding conditions are given. In order to establish the possibility of separation of the lower base, a comparison
of the obtained values of the stress on the bottom plate with the stresses arising in the analogous formulation of the static problem for wedge plate considering its own weight is worked out.
Original languageEnglish
Pages (from-to)4435-4450
Number of pages16
JournalActa Mechanica
Issue number12
Early online date18 Aug 2017
Publication statusPublished - Dec 2017

Bibliographical note

The research is supported by the British Council Ukraine—International higher education (Ref. UKR16EG/28/29.01.16). The authors would like to express their deep gratitude to Mr. Simon P. Dyke for his help in the article’s text editing.


  • wedge shaped thick plate
  • integral transformation
  • one-dimensional vector boundary problem
  • exact solution


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