Thin Rectangular Plates on Elastic Foundation

1952 ◽  
Vol 19 (3) ◽  
pp. 361-368
Author(s):  
H. J. Fletcher ◽  
C. J. Thorne
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Numerical Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Transverse Loads ◽  
Sine Transform ◽  
Special Cases ◽  
Plates On Elastic Foundation

Abstract The deflection of a thin rectangular plate on an elastic foundation is given for the case in which two opposite edges have arbitrary but given deflections and moments. Six important cases of boundary conditions on the remaining two edges are treated. The solution is given for general transverse loads which are continuous in one direction and sectionally continuous in the other. By use of the sine transform the solution is obtained as a single trigonometric series. Numerical solutions are obtained for six special cases.

FREE VIBRATION OF FUNCTIONALLY GRADED THIN RECTANGULAR PLATES RESTING ON WINKLER ELASTIC FOUNDATION WITH GENERAL BOUNDARY CONDITIONS USING RAYLEIGH–RITZ METHOD

2014 ◽  
Vol 06 (04) ◽  
pp. 1450043 ◽  
Author(s):  
S. CHAKRAVERTY ◽  
K. K. PRADHAN
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Power Law ◽  
Ritz Method ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Aspect Ratios ◽  
Winkler Elastic Foundation ◽  
Special Cases

In this paper, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of classical plate theory is investigated. Rayleigh–Ritz method is used to obtain the generalized eigenvalue problem. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of the FG plate are assumed to vary continuously in the thickness direction of the constituents according to power-law form. The objective is to study the effects of constituent volume fractions, aspect ratios and power-law indices on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. Comparison with the results from the existing literature are provided for validation in special cases. Three-dimensional mode shapes are presented for FG square plates having various boundary conditions at the edges for different power-law indices. The present investigation also involves the rectangular FG plate to lay on a uniform Winkler elastic foundation. New results for the eigenfrequencies associated with foundation parameters are also reported here with the validation in special cases after checking a convergence pattern.

Shear Buckling of Rectangular Plates with Mixed Boundary Conditions

1963 ◽  
Vol 14 (4) ◽  
pp. 349-356 ◽  
Author(s):  
I. T. Cook ◽  
K. C. Rockey
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Shear Buckling

SummaryThe paper presents a solution for the buckling under shear of a rectangular plate which is clamped along one edge and simply-supported along the other edges. The authors have also re-examined the case of one pair of opposite edges clamped and the other pair simply-supported.

Buckling Analysis of Thin Functionally Graded Rectangular Plates Resting on Elastic Foundation

2010 ◽  
Author(s):  
Meisam Mohammadi ◽  
A. R. Saidi ◽  
Mehdi Mohammadi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Coupled Equations ◽  
Aspect Ratios ◽  
Special Cases

In the present article, the buckling analysis of thin functionally graded rectangular plates resting on elastic foundation is presented. According to the classical plate theory, (Kirchhoff plate theory) and using the principle of minimum total potential energy, the equilibrium equations are obtained for a functionally graded rectangular plate. It is assumed that the plate is rested on elastic foundation, Winkler and Pasternak elastic foundations, and is subjected to in-plane loads. Since the plate is made of functionally graded materials (FGMs), there is a coupling between the equations. In order to remove the existing coupling, a new analytical method is introduced where the coupled equations are converted to decoupled equations. Therefore, it is possible to solve the stability equations analytically for special cases of boundary conditions. It is assumed that the plate is simply supported along two opposite edges in x direction and has arbitrary boundary conditions along the other edges (Levy boundary conditions). Finally, the critical buckling loads for a functionally graded plate with different boundary conditions, some aspect ratios and thickness to side ratios, various power of FGM and foundation parameter are presented in tables and figures. It is concluded that increasing the power of FGM decreases the critical buckling load and the load carrying capacity of plate increases where the plate is rested on Pasternak in comparison with the Winkler type.

Postbuckling Behavior of Rectangular Plates With Small Initial Curvature Loaded in Edge Compression

1959 ◽  
Vol 26 (3) ◽  
pp. 407-414
Author(s):  
Noboru Yamaki
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Thin Plates ◽  
Large Deflections ◽  
Effective Width ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Initial Curvature ◽  
Special Cases ◽  
Fundamental Equations

Abstract The solution of Marguerre’s fundamental equations for large deflections of thin plates with slight initial curvature is presented for the case of a rectangular plate subjected to edge compression. The problem is solved under eight different boundary conditions, combining two kinds of loading conditions and four kinds of supporting conditions. Numerical solutions are obtained for square plates with and without initial deflection, and the connections of deflection, edge shortening, and effective width of the plate with applied loads are clarified. The solutions here obtained include as special cases those investigated by Levy and Coan.

Some Thin-Plate Problems by the Sine Transform

1951 ◽  
Vol 18 (2) ◽  
pp. 152-156
Author(s):  
L. I. Deverall ◽  
C. J. Thorne
Keyword(s):  
Thin Plate ◽  
The Other ◽  
Rectangular Plates ◽  
Specific Load ◽  
General Solutions ◽  
Arbitrary Load ◽  
Sine Transform ◽  
Edge Conditions ◽  
Method Of Solution ◽  
Load Function

Abstract General expressions for the deflection of thin rectangular plates are obtained for cases in which two opposite edges have arbitrary but given deflections and moments. The sine transform is used as a part of the method of solution, since solutions can be found for an arbitrary load for each set of edge conditions at the other two edges. Even for the classical cases, the use of the sine transform makes the process of solving the problem much easier. The six general solutions given are those which arise from all possible combinations of physically important edge conditions at the other two edges. Solutions for a specific load function can be found by integration or by the use of a table of sine transforms. Tables useful in application of the method to specific problems are included.

A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation

2017 ◽  
Vol 12 (1) ◽  
pp. 9-34 ◽  
Author(s):  
Abdelkarim Benahmed ◽  
Mohammed Sid Ahmed Houari ◽  
Samir Benyoucef ◽  
Khalil Belakhdar ◽  
Abdelouahed Tounsi
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Plates On Elastic Foundation

Development of Hybrid Semi-Analytical and Finite Element Analysis to Calculate Sound Radiation from Vibrating Structure

2013 ◽  
Vol 845 ◽  
pp. 71-75 ◽  
Author(s):  
Azma Putra ◽  
Nurain Shyafina ◽  
Noryani Muhammad ◽  
Hairul Bakri ◽  
Noor Fariza Saari
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Analytical Model ◽  
Complex Geometry ◽  
Sound Radiation ◽  
Vibration Velocity ◽  
Rectangular Plates ◽  
Element Analysis

Simple analytical model of plate dynamics usually applies for rectangular plate with simply supported edges. Analytical model of sound radiation from rectangular plate is also convenient, but not for other geometries and other boundary conditions. This paper presents a hybrid mathematical model which combines a semi-analytical model with the Finite Element Analysis (FEA) method to determine sound radiation from a vibrating structure. The latter is employed to calculate the vibration velocity of a structure with a rather complex geometry. The results are then used as the input in the semi-analytical model to calculate the radiated sound pressure through the Rayleigh integral. Results from the proposed model are presented here for the radiation efficiency of rectangular plates with different boundary conditions.

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