A Thermo-elastic Annular Plate Model for the Modeling of Brake Systems

1. Introduction and Summary. —This paper deals with the elastic stability of a circular annular plate under uniform shearing forces applied at its edges. Investigations of the stability of plane plates are altogether simpler than those necessary in the case of curved plates or shells. In the first place, as shown by Mr. R. V. Southwell, two of the three equations of stability relate to a mode of instability that is not of practical interest, and are entirely independent of the third equation which gives the ordinary mode of instability resulting in the familiar bending of the middle surface of the plate. Consequently with a plane plate there is only one equation of stability to be solved, as contrasted with the case of a shell where the three equations are dependent, and must all be solved. In the second place the theory of thin shells can be used with confidence in a plane plate problem, though a more laborious procedure is necessary to deal adequately with a shell. The only stability equation required for the annular plate is therefore deduced without trouble from the theory of thin shells, and its solution presents no difficulty in the case of uniform shearing forces. A numerical discussion is given of the stability of the plate under such forces, the “favourite type of distortion” and the stess that will produce it being obtained for plates with clamped edges in wich the ratio of the outer to the inner radius exceeds 3·2. To some extent to results have been checked by experiment, in which part of the work the viter is indebted to Prof. G. I. Taylor for his valuable help and advice. Distrtion of the type predicted by the theory took place in the two thin plates of rober different ratio of radii, which were used. The disposition of the loci of points which undergo maximum normal displace nt gives some idea of the appearance of the plate after distortion has taken pce. The points have been calculated for a plate in which the ratio of radii 4·18, and the loci are shown on a diagram, which may be compared with a potograph of a distorted plate in which this ratio is 4·3. The ratio of normal dplacements of points of the plate can be seen from contours drawn on the ne diagram. (See pp. 280, 281.)

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Free Vibration of Functionally Graded Graphene Platelet Reinforced Plates : A Quasi 3D Shear and Normal Deformable Plate Model

Composite Structures ◽

10.1016/j.compstruct.2021.114409 ◽

2021 ◽

pp. 114409

Author(s):

P. Jafari ◽

Y. Kiani

Keyword(s):

Free Vibration ◽

Functionally Graded ◽

Plate Model ◽

Graphene Platelet

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Null controllability of a thermoelastic plate

Abstract and Applied Analysis ◽

10.1155/s108533750220408x ◽

2002 ◽

Vol 7 (11) ◽

pp. 585-599 ◽

Cited By ~ 26

Author(s):

Assia Benabdallah ◽

Maria Grazia Naso

Keyword(s):

Thermal Control ◽

Finite Energy ◽

Null Controllability ◽

Energy Solution ◽

Plate Model ◽

Time And Space ◽

Thermal Equation ◽

Control Time ◽

Thermoelastic Plate ◽

Finite Energy Solution

Thermoelastic plate model with a control term in the thermal equation is considered. The main result in this paper is that with thermal control, locally distributed within the interior and square integrable in time and space, any finite energy solution can be driven to zero at the control timeT.

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Bending of an incomplete annular plate and related problems

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247v143103 ◽

1979 ◽

Vol 14 (3) ◽

pp. 103-109 ◽

Cited By ~ 7

Author(s):

J R Barber

Keyword(s):

Stress Concentration ◽

Closed Form ◽

Circular Plate ◽

Annular Plate ◽

Infinite Plate ◽

Concentration Data ◽

Closed Form Solutions ◽

Concentrated Forces

Closed-form solutions and stress-concentration data are obtained for the problem of a sector of an annular plate subjected to moments and transverse forces on its radial edges. Closed-form solutions are also given for a semi-infinite plate or a circular plate subjected to a system of concentrated forces and/or moments at the edge.

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