Solutions of vibration problems for thin infinite plates subjected to harmonic loads

Research output: Contribution to journalArticleResearchpeer-review

Abstract

New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.
LanguageEnglish
Pages949-961
Number of pages13
JournalJournal of Theoretical and Applied Mechanics
Volume55
Issue number3
StatusPublished - 27 Jul 2017

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Vibration
Harmonic
Kirchhoff Plate
Closed-form Solution
Addition Theorem
Hankel transform
Plate Theory
Particular Solution
Bessel Functions
Closed-form
Partial differential equation
Ring

Keywords

  • Kirchhoff plate theory
  • infinite plate
  • ring load
  • circular load
  • Hankel transform
  • particular solution

Cite this

Solutions of vibration problems for thin infinite plates subjected to harmonic loads. / Klanner, Michael; Ellermann, Katrin.

In: Journal of Theoretical and Applied Mechanics , Vol. 55, No. 3, 27.07.2017, p. 949-961.

Research output: Contribution to journalArticleResearchpeer-review

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