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

Michael Klanner*, Katrin Ellermann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)949-961
Number of pages13
JournalJournal of Theoretical and Applied Mechanics
Issue number3
Publication statusPublished - 27 Jul 2017


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

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