The Bending of Uniformly Loaded Sectorial Plates With Clamped Edges

1952 ◽  
Vol 19 (1) ◽  
pp. 5-8
Author(s):  
H. D. Conway ◽  
M. K. Huang
Keyword(s):  
Circular Plate ◽  
Elementary Solution ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Clamped Edges ◽  
Clamped Edge

Abstract This paper analyzes the bending of a sectorial plate, clamped on all edges and subjected to uniformly distributed load, by using two different methods of superposition on the elementary solution for a uniformly loaded circular plate with a clamped edge.

scholarly journals The Vibrations of a Circular Plate with Uniformly Distributed Load around the Outer Periphery

1973 ◽  
Vol 16 (94) ◽  
pp. 714-723 ◽  
Author(s):  
Shin TAKAHASHI ◽  
Katsuyoshi SUZUKI ◽  
Yoshiharu NAKAMURA
Keyword(s):  
Circular Plate ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Outer Periphery

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

2007 ◽  
Author(s):  
George Weiss
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Bessel Functions ◽  
Unit Area ◽  
Continuous System ◽  
Modified Bessel Functions ◽  
Circular Plates ◽  
Numerical Parameter ◽  
Elliptical Plate ◽  
Distributed Load

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 K02, 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 K02 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.

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