Axially Symmetrical Plates With Linearly Varying Thickness

1951 ◽  
Vol 18 (2) ◽  
pp. 140-142
Author(s):  
H. D. Conway
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Variable Thickness ◽  
Practical Problem ◽  
Constant Thickness ◽  
Circular Plates ◽  
Varying Thickness ◽  
Small Deflection ◽  
Special Case ◽  
Plates Of Variable Thickness

Abstract The most practical problem in the bending of symmetrically loaded circular plates of variable thickness is probably that in which the thickness decreases linearly with the distance from the center of the plate. A general solution of the small-deflection problem of such plates is given here in closed form for the special case when Poisson’s ratio is 1/3. Numerical results are given for two particular examples, and these are compared with the results for corresponding plates of constant thickness.

The Bending of Symmetrically Loaded Circular Plates of Variable Thickness under Uniform Compression

1968 ◽  
Vol 19 (1) ◽  
pp. 59-70
Author(s):  
R. S. Dhaliwal
Keyword(s):  
Variable Thickness ◽  
Circular Ring ◽  
Maximum Deflection ◽  
Circular Plates ◽  
Uniform Compression ◽  
Varying Thickness ◽  
Ring Plate ◽  
Plates Of Variable Thickness

SummaryThe solution has been obtained for the problem of a uniformly compressed and symmetrically loaded circular ring plate of linearly varying thickness. Four particular cases have been discussed and numerical values of the maximum deflection have been obtained for various sizes of the hole of the ring.

Note on the Bending of Circular Plates of Variable Thickness

1949 ◽  
Vol 16 (2) ◽  
pp. 209-210
Author(s):  
H. D. Conway
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Simple Solution ◽  
Central Hole ◽  
Circular Plates ◽  
Special Case ◽  
Plates Of Variable Thickness

Abstract In a recent paper a solution was given to the problem of a symmetrically loaded circular plate with a central hole, the thickness of the plate at any section being proportional to the distance of the section from the center of the plate. A very simple solution can be obtained for another variation of thickness of which the foregoing is a special case.

The Bending of Symmetrically Loaded Circular Plates of Variable Thickness

1948 ◽  
Vol 15 (1) ◽  
pp. 1-6
Author(s):  
H. D. Conway
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Maximum Stress ◽  
Central Hole ◽  
Constant Thickness ◽  
External Diameter ◽  
Circular Plates ◽  
Plates Of Variable Thickness

Abstract This investigation was carried out with the object of obtaining a solution to the problem of a symmetrically loaded circular plate with a central hole, the thickness of the plate at any section being proportional to the distance of the section from the center of the plate. Six particular cases were investigated, and the values of the maximum stress and deflection calculated for various ratios of the external diameter of the plate to the diameter of the central hole. These values were compared with the corresponding values obtained for plates of constant thickness by A. M. Wahl and G. Lobo (1).

Deformations and Stresses in Symmetrically Loaded Circular Plates of Varying Thickness

1953 ◽  
Vol 57 (511) ◽  
pp. 449-454 ◽  
Author(s):  
D. C. Boston
Keyword(s):  
Temperature Gradient ◽  
Gas Turbine ◽  
Variable Thickness ◽  
Material Properties ◽  
Simple Function ◽  
Constant Thickness ◽  
Circular Plates ◽  
Strength Of Materials ◽  
Varying Thickness

The problem of symmetrically loaded circular plates of constant thickness is covered adequately in several of the standard textbooks on the strength of materials. Formulae are derived enabling the deflections and stresses to be readily calculated in any portion of the plate. The problem is complicated by the introduction of a variable thickness and by a variation of material properties due to a temperature gradient down the radius of the plate; conditions such as are encountered in gas turbine wheels, bearing support diaphragms and flexible disc couplings. Methods exist whereby the plate can be solved if the thickness is a simple function of the plate radius, but in practice this is not always so, the profile often being complicated by flanges and spigots.

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

scholarly journals Natural frequencies of orthotropic circular plates of variable thickness.

AIAA Journal ◽  
1968 ◽  
Vol 6 (8) ◽  
pp. 1625-1626 ◽  
Author(s):  
ALAN P. SALZMAN ◽  
SHARAD A. PATEL
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Circular Plates ◽  
Plates Of Variable Thickness

RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

2021 ◽  
Vol 98 (6) ◽  
pp. 36-42
Author(s):  
A.V. TURKOV ◽  
◽  
S.I. POLESHKO ◽  
E.A. FINADEEVA ◽  
K.V. MARFIN ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Circular Plates ◽  
Outer Contour ◽  
Numerical Studies ◽  
The Difference ◽  
Relationship Of ◽  
The Relationship ◽  
Hinged Support ◽  
Natural Transverse

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

Large Deflections of Circular Plates of Variable Thickness

1982 ◽  
Vol 49 (1) ◽  
pp. 243-245 ◽  
Author(s):  
B. Banerjee
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Deflection ◽  
Numerical Results ◽  
Large Deflections ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

Sign in / Sign up

Export Citation Format

Share Document