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

[+] Author Affiliations
George Weiss

Weiss Consultants, Rego Park, NY

Paper No. IMECE2007-41018, pp. 527-530; 4 pages
doi:10.1115/IMECE2007-41018
From:
  • ASME 2007 International Mechanical Engineering Congress and Exposition
  • Volume 10: Mechanics of Solids and Structures, Parts A and B
  • Seattle, Washington, USA, November 11–15, 2007
  • Conference Sponsors: ASME
  • ISBN: 0-7918-4304-1 | eISBN: 0-7918-3812-9
  • Copyright © 2007 by ASME

abstract

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

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