Journal of Theoretical
and Applied Mechanics

55, 3, pp. 949-961, Warsaw 2017
DOI: 10.15632/jtam-pl.55.3.949

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

Michael Klanner, Katrin Ellermann
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.
Keywords: Kirchhoff plate theory, infinite plate, ring load, circular load, Hankel transform