ON AN ELLIPTICAL PLATE FLUTTER

Abstract A solution is obtained by means of the Ritz method for the “large-deflection” problem of a clamped elliptical plate of constant thickness, subjected to a uniformly distributed load. Two shapes of elliptical plate are treated, in addition to the limiting cases of the circular plate and infinite strip, for which the exact solutions are known. Center deflections as well as total stresses at the center and edge decrease as one proceeds from the infinite strip through the elliptical shapes to the circular plate, holding the width of the plates constant. The relation between edge-stress at the semiminor axis (maximum stress in the plate) and center deflection is found to be practically independent of the proportions of the elliptical plate. Hence the governing stress may be determined from a single curve for a given load on an elliptical plate of arbitrary dimensions, if the center deflection is known.

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

Volume 10: Mechanics of Solids and Structures, Parts A and B ◽

10.1115/imece2007-41018 ◽

2007 ◽

Cited By ~ 1

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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Positioning Effect on Free Convection with an Elliptical Plate Placed in a Circular Enclosure

Advanced Science Engineering and Medicine ◽

10.1166/asem.2020.2668 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1054-1062

Author(s):

Parth Patpatiya ◽

Soumya ◽

Bhavya Shaan ◽

Bhavana Yadav

Keyword(s):

Heat Transfer ◽

Aspect Ratio ◽

The Body ◽

Elliptical Plate ◽

Numerical Studies ◽

First Case ◽

Varied Temperature ◽

Laminar Natural Convection ◽

The Given ◽

Plate System

In this analysis we have examined the process of the steady state laminar natural convection around heated elliptical plate with Rayleigh number 10^6 positioned inside a circular enclosure. The purpose of the numerical analysis is to analyze the behavior of isotherms, streamlines and heat transfer rate in enclosure plate system due to the variation in the position of elliptical plate (r/D =0.00, 0.05, and 0.2) and aspect ratio, where the given diameter of the enclosure is D and r is the distance between the centre of elliptical plate and centre of circle. Elliptical plate is inclined at different angles and results are summed up in relative manner. There are two cases, in first case aspect ratio a/D and b/D is varied and D is kept constant, whereas in second case aspect ratio a/D and b/D is kept constant and D is varied. Temperature difference between the enclosure and the inner body (i.e., temperature of inner body is kept high as compared to the enclosure) is maintained. Two dimensional study is followed by considering air as a fluid in enclosure. The effects of the Heat Transfer and Flow of Fluid are analyzed by the streamlines and isotherms plotted for the body placed inside enclosure. Value of local Nusselt number (Nu) is also plotted along the wall of elliptical plate and along the surface of the circular enclosure. For every aspect ratio isotherms and streamlines had been plotted. This work has been validated with various other numerical studies and was in good conciliation.

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Delamination-Free Drilling of Composite Laminates

Journal of Engineering for Industry ◽

10.1115/1.2902131 ◽

1994 ◽

Vol 116 (4) ◽

pp. 475-481 ◽

Cited By ~ 106

Author(s):

S. Jain ◽

D. C. H. Yang

Keyword(s):

Composite Laminates ◽

Thrust Force ◽

Tool Geometry ◽

Elliptical Plate ◽

Hole Quality ◽

Drilling Operation ◽

Twist Drills ◽

Drill Tool

Composite laminates in significant numbers are rendered unacceptable due to delamination that occurs during the drilling operation. Thrust generated during the drilling operation is identified as responsible for delamination. Expressions developed for critical thrusts and critical feed rates, by modeling the delamination zone as an elliptical plate in unidirectional laminates, appear to be fairly accurate. It has been demonstrated that the critical thrusts and feed rates obtained for unidirectional laminates can be conservatively used for multi-directional laminates. With regard to the tool geometry, the chisel edge width appears to be the single most important factor contributing to the thrust force and hence delamination. A diamond-impregnated tubular drill tool was designed and tested. This tool resulted in a much smaller thrust and much better hole quality as compared with the standard twist drills.

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