• DOI:10.1115/IMECE2007-41018
• Corpus ID: 122067748

Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge

@inproceedings{Weiss2007ApproximatedFF,
  title={Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge},
  author={George Weiss},
  year={2007}
}

• G. Weiss
• Published 2007
• Engineering

Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate itself. Considering the mass per unit area of the plate, and substituting it in Dunkerley’s equation rearranged, we obtain a numerical parameter K0 2 , related to the fundamental frequency of the plate, which has to be evaluated for each particular case. In this paper, have been evaluated the values of K0 2 for thin circular plates clamped or pinned at edge. An elliptical plate clamped at edge is also presented for several ratios of the semi–axes, one of which is identical with a circular plate.Copyright © 2007 by ASME