On Natural Frequencies of Geometrically Imperfect, Simply-Supported Rectangular Plates Under Uniaxial Compressive Loading

1991 ◽  
Vol 58 (4) ◽  
pp. 1082-1084 ◽  
Author(s):  
S. Ilanko ◽  
S. M. Dickinson
Keyword(s):  
Natural Frequencies ◽  
Compressive Loading ◽  
Rectangular Plates ◽  
Simply Supported

BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES

2001 ◽  
Vol 01 (03) ◽  
pp. 385-408 ◽  
Author(s):  
Y. XIANG ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
The Other ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Step Thickness ◽  
Thickness Variations

This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates 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 proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

Vibration of Centrally Stiffened Rectangular Plate

1961 ◽  
Vol 65 (610) ◽  
pp. 695-697 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Empirical Method ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Stiffening Ribs ◽  
Square Plate ◽  
Semi Empirical

Natural frequencies of free flexural vibration of rectangular plates may, in many cases, be considerably increased by attaching to the plate one or more elastic stiffening ribs parallel to one edge, or by casting or machining the plate and stiffeners integrally.Hoppmann has determined by a semi-empirical method the natural frequencies of an integrally stiffened simply-supported square plate, using the concept of a homogeneous orthotropic plate of uniform thickness having elastic compliances which are equivalent to those of the stiffened plate. Filippov has obtained the exact solution for the fundamental frequency of a simply-supported square plate having a number of equally spaced stiffeners and has considered the effect of point loads applied to the stiffeners in a direction perpendicular to the plane of the plate.

Free Oscillations of Edge-Connected Simply Supported Plate Systems

1961 ◽  
Vol 83 (4) ◽  
pp. 434-439 ◽  
Author(s):  
Eric E. Ungar
Keyword(s):  
Individual Component ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Free Oscillations ◽  
Common Edge ◽  
Simply Supported ◽  
The Individual ◽  
Plate System

A simple semigraphical method for calculating the natural frequencies of two-plate systems is developed, a two-plate system being one made up of two rectangular plates simply supported at all edges and joined at a common edge. Charts for easy determination of the afore-mentioned natural frequencies are developed. One of these gives, as a by-product, the natural frequencies of rectangular plates (of any dimensions) having one edge clamped, the remaining three simply supported. It is demonstrated that the higher natural frequencies of two-plate systems are very nearly equal to those of the individual component plates. Equations for the mode shapes are also given.

Flexural Vibration of Rectangular Plates with Stiffeners Parallel to the Edges

1963 ◽  
Vol 67 (634) ◽  
pp. 664-668 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequencies ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Equivalent System ◽  
Simply Supported ◽  
Finite Difference Equations ◽  
Four Corners

SummaryThe basis of the procedure described in the paper is the replacement of the stiffeners by an approximately equivalent system of line springs. One of two methods may then be used to determine the natural frequencies. A rectangular plate with edge stiffeners, point-supported at the four corners, is used to demonstrate the application of the Rayleigh-Ritz method. Numerical results obtained are compared with known approximate solutions based on finite difference equations. A Holzer-type iteration is employed in the case of a plate with parallel stiffeners, where the two edges perpendicular to the stiffeners are simply supported, the other two edges having any combination of conditions.

Vibration of Stiffened Plates

1964 ◽  
Vol 15 (3) ◽  
pp. 285-298 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
General Procedure ◽  
The Other ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions

SummaryThis paper presents a general procedure for calculating the natural frequencies of rectangular plates continuous over identical and equally spaced elastic beams which are simply-supported at their ends. Arbitrary boundary conditions are permissible on the other two edges of the plate. The results are compared with those obtained by using the orthotropic plate approximation for the system

scholarly journals DYNAMICS OF RECTANGULAR ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL – GALERKIN’S METHODS

2016 ◽  
Vol 36 (1) ◽  
pp. 50-56
Author(s):  
NN Osadebe ◽  
CM Attama ◽  
OA Oguaghamba
Keyword(s):  
Orthogonal Polynomial ◽  
Rectangular Plate ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Trial And Error ◽  
Shape Functions ◽  
Orthotropic Plates ◽  
Approximate Methods ◽  
Simply Supported ◽  
Polynomial Theory

The assumed deflection shapes used in the approximate methods such as in the Galerkin’s method were normally formulated by inspection and sometimes by trial and error, until recently, when a systematic method of constructing such a function in the form of Characteristic Orthogonal Polynomial (COPs) was developed by Bhat in 1985. In the vibrational analyses of orthotropic rectangular plates with different boundary conditions, the study used the characteristic orthogonal polynomial theory to obtain satisfactory approximate shape functions for these plates. These functions were applied to Galerkin indirect varational method to obtain new set of fundamental natural frequencies for these plates. The results were reasonable when compared with those in the previous work. All round simply supported thin rectangular plate (SSSS), rectangular clamped plated (CCCC) and rectangular plate with one edge clamped and all others edges simply supported (CSSS) gave 5.172, 9.429 and 6.202 natural frequencies in rad /sec respectively at 0.05%, 0.0% and 22.93% difference with the previous[3] results5.170rad/sec, 9.429rad/sec and 8.048rad/sec  for SSSS, CCCC and CSSS. For others like: rectangular plate with one edge simply supported and all other edges clamped (CCSC), rectangular plate simply supported at two opposite sides and clamped at the others (CSCS) and rectangular plate clamped at two adjacent sides and simply supported at the others (CCSS) with no available results, their natural frequencies obtained are 8.041rad/sec, 6.272rad/sec and 7.106rad/sec respectively. http://dx.doi.org/10.4314/njt.v36i1.8

Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

1997 ◽  
Vol 122 (1) ◽  
pp. 77-81 ◽  
Author(s):  
C. M. Wang ◽  
S. Kitipornchai ◽  
J. N. Reddy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Kirchhoff Plate ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Third Order ◽  
Simply Supported ◽  
Kirchhoff Plate Theory ◽  
The Relationship ◽  
Exact Relationship

This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]

The Natural Frequency of Vibration of Curved Rectangular Plates

1954 ◽  
Vol 5 (2) ◽  
pp. 101-110 ◽  
Author(s):  
P. J. Palmer
Keyword(s):  
Natural Frequency ◽  
Pressure Wave ◽  
Natural Frequencies ◽  
Dynamic Pressure ◽  
Mode Frequency ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Pressure

SummaryThe natural frequency of vibration of curved rectangular plates, with both simply-supported and fixed edges, is evaluated for the fundamental extensional mode. This mode is thought to be applicable when the plates are excited by a uniformly distributed pressure as may occur with a dynamic pressure wave. The natural frequencies corresponding to this mode increase fairly rapidly with the curvature of the plate.The natural frequency of vibration of the plates when the mode is the fundamental inextensional mode is also considered. The frequency of this mode is higher than that of the extensional mode for small curvatures, but the inextensional mode frequency falls slowly with increase in curvature of the plate. Thus, if the curvature of the plate is sufficiently large, the frequency of the fundamental inextensional mode is lower than that of the extensional mode.

Carrying capacity of edge-compressed rectangular plates

1980 ◽  
Vol 7 (1) ◽  
pp. 19-26
Author(s):  
A. N. Sherbourne ◽  
H. M. Haydl
Keyword(s):  
Carrying Capacity ◽  
Ultimate Load ◽  
Compressive Loading ◽  
Effective Width ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Simply Supported ◽  
Elastic Loading ◽  
Special Case ◽  
Good Agreement

The carrying capacity of simply supported rectangular plates under uniaxial, in-plane compressive loading is investigated. The ultimate load is determined as the load corresponding to the intersection of an elastic loading line and a rigid–plastic unloading line. An attempt is made to formulate a plastic roof mechanism for the rectangular plate; the square buckle pattern mechanism for long plates is obtained as a special case. The effective width method is re-examined and is shown to give good agreement with experimental evidence. The recommendations of CSA S136-1974 are briefly reviewed in the light of the results obtained.

Bending of Elastically Restrained Rectangular Plates Under Uniform Pressure

1958 ◽  
Vol 62 (575) ◽  
pp. 834-836 ◽  
Author(s):  
C. Lakshmi Kantham
Keyword(s):  
Natural Frequencies ◽  
Unit Length ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Edge Conditions ◽  
Definition Of ◽  
Elastically Restrained ◽  
Clamped Edges ◽  
Clamped Edge

In the bending and vibration of plates it is found that the values of maximum deflection and natural frequencies, respectively, vary considerably from the simply-supported to clamped edge conditions. For an estimation of these characteristics in the intermediate range a generalised boundary condition may be assumed, of which the simply-supported and clamped edges become limiting cases. While Bassali considers the ratio of edge moment to the cross-wise moment as a constant, Newmark, Lurie and Klein and other investigators, in their analyses of various structures, consider that moment and slope at an end are proportional.Here the definition of elastic restraint as given by Timoshenko, α=βM, is followed, where α is the slope at any edge, M the corresponding edge moment per unit length while β is the elastic restraint factor. β→0 and β→∞ represent the two limiting cases of simply-supported and clamped edge conditions.

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