Loss factor for a simply supported rectangular plate of variable thickness

AIAA Journal ◽  
1975 ◽  
Vol 13 (9) ◽  
pp. 1228-1230
Author(s):  
S. P. Nigram ◽  
G. K. Grover ◽  
S. Lal
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Loss Factor ◽  
Simply Supported ◽  
Plate Of Variable Thickness

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

Buckling of Rectangular Plates With General Variation in Thickness

1973 ◽  
Vol 40 (3) ◽  
pp. 745-751 ◽  
Author(s):  
D. S. Chehil ◽  
S. S. Dua
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Perturbation Technique ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Bending Vibration ◽  
Simply Supported ◽  
Buckling Stress ◽  
General Variation ◽  
Plate Of Variable Thickness

A perturbation technique is employed to determine the critical buckling stress of a simply supported rectangular plate of variable thickness. The differential equation is derived for a general thickness variation. The problem of bending, vibration, buckling, and that of dynamic stability of a variable thickness plate can be deduced from this equation. The problem of buckling of a rectangular plate with simply supported edges and having general variation in thickness in one direction is considered in detail. The solution is presented in a form such as can be easily adopted for computing critical buckling stress, once the thickness variation is known. The numerical values obtained from the present analysis are in excellent agreement with the published results.

Stress and deformation of a loaded rectangular plate of variable thickness

1989 ◽  
Vol 25 (8) ◽  
pp. 757-763
Author(s):  
Yu. N. Nemish ◽  
V. P. Maslov ◽  
I. S. Sagalyuk ◽  
D. I. Chernopiskii
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Plate Of Variable Thickness ◽  
Stress And Deformation

Loss Factor for a Rectangular Plate of Parabolic Thickness Variation

1977 ◽  
Vol 99 (3) ◽  
pp. 799-801
Author(s):  
S. P. Nigam ◽  
G. K. Grover ◽  
S. Lal
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Fundamental Mode ◽  
Loss Factor ◽  
Thickness Variation ◽  
Stress System ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Aspect Ratios ◽  
Mode Loss

The importance of the internal damping and of the evaluation of the fundamental mode loss factor of structural members subjected to multiaxial stress system is well known. A good amount of work is available on the elastic vibrations of ectangular plates of uniform thickness but it appears that little work has been done on vibrations of rectangular plates of variable thickness, though such cases are of interest in the aeronautical field since they approximate to wing sections. In the present work, the fundamental mode loss factors for a simply supported rectangular plate with parabolic thickness variation in X direction have been evaluated for different combinations of the aspect ratios and the taper parameters. An approximate relationship has been obtained which correlates the loss factor for the plate of variable thickness with that of a plate of uniform thickness.

Triangular finite elements of variable thickness and their application to plate and shell problems

1969 ◽  
Vol 4 (1) ◽  
pp. 10-21 ◽  
Author(s):  
R Dungar ◽  
R T Severn
Keyword(s):  
Variable Thickness ◽  
Hybrid Approach ◽  
Experimental Tests ◽  
Free Edge ◽  
Beam Element ◽  
Simply Supported ◽  
Plate And Shell ◽  
Mass Matrices ◽  
Finite Element Calculations ◽  
Plate Of Variable Thickness

Stiffness and mass matrices are discussed for a plane triangle whose thickness is allowed to vary linearly between the nodes. In-plane and bending actions are considered separately, and the formulation makes use of the ‘hybrid’ approach, in which the from of the stresses is assumed inside, and on the boundary of, the triangle, and displacements additionally assumed on the boundary only. In Appendix 1 the hybrid approach is developed in detail for a simple beam element. The allowance of variable thickness carries with it a greater reliance on efficient use of computers, and an opportunity is taken in the paper to reorganize the hybrid approach to achieve this. The accuracy attainable with this new element is assessed by comparison with results obtained by other methods for a flat plate of variable thickness, simply supported along its edges. A similar plate supported at its corners, and containing holes, is also considered, and the finite-element calculations are compared with moiré fringe and other experimental tests. A simple vibration problem is also discussed. Finally, the problem of a free-edge boundary is considered. In previous studies spurious stresses were calculable on such boundaries. By employing special elements in these regions the required stresses are made indentically zero.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

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