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.

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.

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.

Deflection and Moment Data for Rectangular Plates of Variable Thickness

1972 ◽  
Vol 39 (3) ◽  
pp. 814-815 ◽  
Author(s):  
P. Petrina ◽  
H. D. Conway
Keyword(s):  
Variable Thickness ◽  
Rectangular Plates ◽  
Direction Parallel ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Plates Of Variable Thickness

Numerical values of deflections and moments are given for uniformly loaded rectangular plates with a pair of opposite sides simply supported and the others either simply supported or clamped. The plates are tapered in a direction parallel to the simply supported sides. Data are given for two tapers and for plate aspect ratios equal to 1 (square plates), 1.5 and 2.

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.

scholarly journals Analysis of inelastic buckling of rectangular plates with a free edge using polynomial deflection functions

2020 ◽  
Vol 11 (1) ◽  
pp. 15-21
Author(s):  
Uchechi G. Eziefula
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Polynomial Function ◽  
Free Edge ◽  
Rectangular Plates ◽  
Maclaurin Series ◽  
Inelastic Buckling ◽  
Aspect Ratios ◽  
Isotropic Plates ◽  
Deformation Plasticity

AbstractThe inelastic buckling behaviour of different rectangular thin isotropic plates having a free edge is studied. Various combinations of boundary conditions are subject to in-plane uniaxial compression and each rectangular plate is bounded by an unloaded free edge. The characteristic deflection function of each plate is formulated using a polynomial function in form of Taylor–Maclaurin series. A deformation plasticity approach is adopted and the buckling load equation is modified using a work principle technique. Buckling coefficients of the plates are calculated for various aspect ratios and moduli ratios. Findings obtained from the investigation are found to reasonably agree with data published in the literature.

Large Deflections of Rectangular Plates

1971 ◽  
Vol 15 (02) ◽  
pp. 164-171
Author(s):  
Norman Jones ◽  
R. M. Walters
Keyword(s):  
Approximate Method ◽  
Rectangular Plate ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Finite Deflections ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Plastic Analysis ◽  
Theoretical Procedure

An approximate rigid, perfectly plastic analysis which retains the influence of finite deflections is presented herein for a uniformly loaded, fully clamped rectangular plate. This theoretical procedure provides reasonable engineering estimates of the permanent deflections of rectangular plates according to the recent experiments of Hooke and Rawlings on plates with aspect ratios in the range 1/3 ≤ β ≤ 1. The approximate method also predicts values which agree fairly well with the tests of Young on long rectangular plates β = 1/3), and for large permanent deflections gives similar values to the analysis by Greenspon when β = 1.

Simulation of Planarization of Rectangular Glass Plate Using Tool-Path-Control-Type Polishing

2009 ◽  
Vol 76-78 ◽  
pp. 313-318
Author(s):  
Kenichiro Yoshitomi ◽  
Atsunobu Une ◽  
Masaaki Mochida
Keyword(s):  
Rectangular Plate ◽  
Tool Path ◽  
Liquid Crystal Display ◽  
Glass Plate ◽  
Rectangular Plates ◽  
Short Side ◽  
Aspect Ratios ◽  
Path Control ◽  
Rotary Type ◽  
Rectangular Glass

The size of the photo mask and mother glass used in liquid crystal display production has increased yearly. Large rectangular glass plates are difficult to planarize using rotary-type polishing machines. We have developed a rotary-type polishing machine with tool path control that is optimized by polishing simulation for a rectangular wafer. The present paper describes the planarization of a rectangular plate by simulation. The influence of tool size and the aspect ratio of the rectangular plate on the flatness are clarified. For a square plate, the flatness obtained under optimized oscillation speed is less than a quarter of that obtained under uniform oscillation speed. For rectangular plates with aspect ratios of 1:1.25 and 1:1.5, planarization using a tool having a diameter equal to half the diagonal length of the plate is shown to be difficult because the stock removal distributions in diagonal and short side of the workpiece become the different shape.

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

Study on the Use of Boundary Characteristic Orthogonal Polynomials in Determining the Fundamental Frequency of Rectangular Plates with Bidirectional Linear Thickness Variation

2016 ◽  
Vol 852 ◽  
pp. 518-524
Author(s):  
Tanmay Gupta ◽  
Bhagat Kewlani ◽  
Kiran D. Mali
Keyword(s):  
Boundary Conditions ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Shape Function ◽  
Two Dimensions ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Geometric Boundary ◽  
Boundary Characteristic

Free vibration of rectangular plates with linearly varying thickness is considered. Plates are important structural components used in aircrafts, bridges etc. and hence for their safe design, thorough vibration analysis is important. Many research and practical applications use plates of variable thickness due to economical usage of the material and increased strength. Vibration response of these types of plates is different from plates of uniform thickness, which makes their analysis critical. In this study, Boundary Characteristic Orthogonal Polynomials (BCOPs) in one and two dimensions have been used to obtain deflection shape function. The first member of the series is generated using the boundary conditions, in this case all edges clamped, which satisfies both the geometric boundary conditions and the natural boundary conditions. Gram Schmidt Orthogonalization for polynomials is used to generate the higher members of the shape function which only satisfy the geometric boundary conditions. Thickness variation considered for the plate is linear in both x and y direction. Natural frequencies were obtained by using Rayleigh-Ritz method. Natural frequencies were calculated by varying taper parameters for both directions and compared with those obtained with the case of uniform thickness. Natural frequencies were also found comparable with those obtained from Finite Element Analysis by using ANSYS.

Vibration of Rectangular Plates of Variable Thickness

1966 ◽  
Vol 8 (1) ◽  
pp. 42-51 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Finite Element ◽  
Variable Thickness ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
The Finite Element Method ◽  
Uniform Thickness ◽  
Isotropic Rectangular Plate ◽  
Vibration Problems ◽  
Rectangular Plate Element ◽  
Plates Of Variable Thickness

In a previous paper the application of the finite element method to plate vibration problems was discussed. It was shown that the method gave good results when applied to the vibration of plates of uniform thickness. The present paper extends the method to include plates of variable thickness. In particular stiffness and inertia matrices are derived for an isotropic rectangular plate element of linearly variable thickness in one co-ordinate direction. These matrices are used to find the natural frequencies and mode shapes of a number of rectangular planform cantilever plates of non-uniform thickness. Experimental results provide a basis for comparison with the finite element results.

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