On the Deflection of Rectangular Orthotropic Plates Under Lateral Loads

1964 ◽  
Vol 68 (643) ◽  
pp. 483-484
Author(s):  
N. R. Rajappa
Keyword(s):  
Isotropic Plate ◽  
The Other ◽  
Rectangular Plates ◽  
Lateral Loads ◽  
Orthotropic Plates ◽  
Characteristic Equations ◽  
Simply Supported ◽  
Elastically Restrained ◽  
Two Sides

Recently the use of Maclaurin’s series was illustrated for the analysis of orthotropic plates. Formulae connecting the deflection of orthotropic plates to that of the corresponding isotropic plate are established here, thus eliminating the need for solving the characteristic equations of orthotropic plates. Rectangular plates with two opposite sides simply-supported and one of the other two sides elastically restrained against rotation are considered.

DSC ANALYSIS FOR BUCKLING AND VIBRATION OF RECTANGULAR PLATES WITH ELASTICALLY RESTRAINED EDGES AND LINEARLY VARYING IN-PLANE LOADING

2009 ◽  
Vol 09 (03) ◽  
pp. 511-531 ◽  
Author(s):  
S. K. LAI ◽  
Y. XIANG
Keyword(s):  
Numerical Stability ◽  
The Other ◽  
Rectangular Plates ◽  
Dsc Analysis ◽  
Vibration Problems ◽  
Discrete Singular Convolution ◽  
Dsc Method ◽  
Elastically Restrained Edges ◽  
Elastically Restrained ◽  
Two Sides

This paper presents the discrete singular convolution (DSC) method for solving buckling and vibration problems of rectangular plates with all edges transversely supported and restrained by uniform elastic rotational springs. The opposite plate edges are subjected to a linearly varying uni-axial in-plane loading. The rationale for using DSC method stems from its numerical stability and flexible implementation for structural analysis. To verify the present approach, convergence and comparison studies for rectangular plates with different combinations of elastically restrained and classical edges are carried out. Accurate buckling and vibration solutions of plates having two opposite edges elastically restrained and the other two sides clamped, or all edges elastically restrained are presented.

BUCKLING AND VIBRATION OF ORTHOTROPIC PLATES WITH AN INTERNAL LINE HINGE

2002 ◽  
Vol 02 (04) ◽  
pp. 457-486 ◽  
Author(s):  
P. R. GUPTA ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
The Other ◽  
Internal Line ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Decomposition Technique ◽  
Orthotropic Plates ◽  
Buckling Loads ◽  
Simply Supported

This paper presents the exact buckling loads and vibration frequencies of orthotropic rectangular plates with internal line hinge and having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is employed to determine the buckling loads and natural frequencies of rectangular plates with internal line hinge.

Some Observations on the Compressive Buckling of Rectangular Plates

1963 ◽  
Vol 14 (1) ◽  
pp. 17-30 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Rate Of Change ◽  
Infinite Strip ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Stress Coefficient ◽  
Wide Range ◽  
Elastically Restrained

SummaryThe problem considered is the buckling of a rectangular plate under uniaxial compression. The ends may be either both clamped, both simply-supported or a mixture of the two. The sides may be elastically restrained against both deflection and rotation with any stiffnesses whatsoever. It is shown that the curve of buckling stress coefficient versus side ratio can be deduced in a simple manner from that of a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength for an infinite strip with the same side conditions are known. Some correlations between the curves for the three types of end condition are discussed. It is also shown that if, for some given side ratio, the buckling mode is known, then it is always possible to deduce the rate of change of buckling stress coefficient with side ratio at that point. The argument is based upon an assumption which is shown to give very accurate results in a wide range of cases.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

Flexural Vibrations of Rectangular Plates

1956 ◽  
Vol 23 (3) ◽  
pp. 430-436
Author(s):  
R. D. Mindlin ◽  
A. Schacknow ◽  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Classical Theory ◽  
The Other ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Rotatory Inertia ◽  
Simply Supported ◽  
Independent Families ◽  
Flexural Vibrations ◽  
Elastically Supported

Abstract The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.

Forced Vibrations of Thin, Elastic, Rectangular Plates with Edges Elastically Restrained Against Rotation

1977 ◽  
Vol 21 (01) ◽  
pp. 24-29
Author(s):  
E. A. Susemihl ◽  
P. A. A. Laura
Keyword(s):  
Bending Moment ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions ◽  
Approach Infinity ◽  
Square Plate ◽  
Elastic Rectangular Plate ◽  
Elastically Restrained ◽  
The Galerkin Method

Polynomial coordinate functions and the Galerkin method are used to determine the response of a thin, elastic, rectangular plate with edges elastically restrained against rotation and subjected to sinusoidal excitation. It is shown that when the flexibility coefficients approach infinity (simply supported edge conditions) the calculated results practically coincide with the exact solution in the case of a square plate when four terms of the expansion are used. Dynamic displacement and bending moment amplitudes are tabulated for different length-to-width ratios, flexibility coefficients, and frequency values.

On Vibrations of Pretwisted Rectangular Plates

1962 ◽  
Vol 29 (1) ◽  
pp. 30-32 ◽  
Author(s):  
R. P. Nordgren
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Numerical Results ◽  
The Other ◽  
Torsional Vibrations ◽  
Rectangular Plates ◽  
Simply Supported

This paper contains an analysis of the free vibrations of uniformly pretwisted rectangular plates, utilizing the exact equations of classical shallow-shell theory. Specifically, solutions are given (a) for two opposite edges simply supported and the other two free, and (b) for all four edges simply supported. Numerical results obtained for case (b) are compared with previous results for the torsional vibrations of pretwisted beams. A simple frequency equation is obtained for case (b), permitting a detailed study of the effects of both pretwist and longitudinal inertia.

Effect of Nonhomogeneity on Vibration of Orthotropic Rectangular Plates of Varying Thickness Resting on Pasternak Foundation

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Roshan Lal ◽  
Dhanpati
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
The Other ◽  
Thickness Variation ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness ◽  
Aspect Ratios ◽  
Displacement Mode

Free transverse vibrations of nonhomogeneous orthotropic rectangular plates of varying thickness with two opposite simply supported edges (y=0 and y=b) and resting on two-parameter foundation (Pasternak-type) have been studied on the basis of classical plate theory. The other two edges (x=0 and x=a) may be any combination of clamped and simply supported edge conditions. The nonhomogeneity of the plate material is assumed to arise due to the exponential variations in Young’s moduli and density along one direction. By expressing the displacement mode as a sine function of the variable between simply supported edges, the fourth order partial differential equation governing the motion of such plates of exponentially varying thickness in another direction gets reduced to an ordinary differential equation with variable coefficients. The resulting equation is then solved numerically by using the Chebyshev collocation technique for two different combinations of clamped and simply supported conditions at the other two edges. The lowest three frequencies have been computed to study the behavior of foundation parameters together with other plate parameters such as nonhomogeneity, density, and thickness variation on the frequencies of the plate with different aspect ratios. Normalized displacements are presented for a specified plate. A comparison of results with those obtained by other methods shows the computational efficiency of the present approach.

Stability of Rectangular Plates Under Shear and Bending Forces

1936 ◽  
Vol 3 (4) ◽  
pp. A131-A135 ◽  
Author(s):  
Stewart Way
Keyword(s):  
Critical Load ◽  
Rectangular Plate ◽  
Bending Moment ◽  
The Other ◽  
Rectangular Plates ◽  
Bending Stress ◽  
Simply Supported ◽  
Tension And Compression ◽  
The Way

Abstract The author first discusses the problem of a plane, simply supported rectangular plate loaded by shearing forces in the plane of the plate on all four edges. There are two stiffeners attached one third and two thirds of the way along the plate. The critical load is calculated for various stiffener rigidities. Also, the rigidity necessary to keep the stiffeners straight when the plate buckles is found. This stiffener rigidity is found to be slightly larger than that necessary for a plate with one stiffener and the same panel dimensions as the plate with two stiffeners. The second problem discussed by the author is that of a plane, simply supported rectangular plate loaded by uniformly distributed edge shearing forces in the plane of the plate and linearly distributed tension and compression in the plane of the plate at the ends. The end forces vary from tension hσo, at one corner to—hσo, at the other corner, so that their resultant is a bending moment. The presence of the edge shearing forces is found to diminish the critical bending stress in this case. Calculations are made for various magnitudes of bending and shearing forces for plates of various proportions.

Sign in / Sign up

Export Citation Format

Share Document