Free Vibration of Rectangular Plates Stiffened With Viscoelastic Beams

1985 ◽  
Vol 52 (2) ◽  
pp. 397-401 ◽  
Author(s):  
K. Ohtomi
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Convenient Method ◽  
Laplace Transformation ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Rectangular Plates ◽  
Dirac Delta ◽  
Simply Supported ◽  
Delta Functions

This investigation treats the free vibration of a simply supported rectangular plate, stiffened with viscoelastic beams. Using a convenient method in which the effects of beams are expressed with Dirac delta functions, the equation of motion can be expressed by only one equation. The frequency equation is obtained by applying the Laplace transformation to the equation of motion. The effects of the volume and the number of beams on the frequency and the logarithmic decrement are clarified.

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.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

Heat Induced Vibration of a Rectangular Plate

1974 ◽  
Vol 96 (3) ◽  
pp. 1015-1021 ◽  
Author(s):  
N. D. Jadeja ◽  
Ta-Cheng Loo
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Rectangular Plate ◽  
Equation Of Motion ◽  
The Other ◽  
Double Trigonometric Series ◽  
Deflection Curve ◽  
Thermally Induced ◽  
Simply Supported ◽  
Governing Differential Equation

The purpose of this paper is to investigate thermally induced vibration of a rectangular plate with one edge fixed and other three edges simply supported. The plate was subjected to a sinusoidal heat input, which varied with respect to time, on one face while the other face of the plate was insulated. An approximate solution to the governing differential equation of motion of the plate was assumed in the form of a double trigonometric series which satisfied all the boundary conditions. Galerkin’s method was then used to obtain the deflection curve for the plate and corresponding stresses at various points in the plate. Certain interesting phenomena indicate the possibility of predicting early fatigue failure. Results are presented in graph forms and discussed.

Fundamental Frequency of Simply Supported Rectangular Plates With Linearly Varying Thickness

1965 ◽  
Vol 32 (1) ◽  
pp. 163-168 ◽  
Author(s):  
F. C. Appl ◽  
N. R. Byers
Keyword(s):  
Rectangular Plate ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness

Upper and lower bounds for the fundamental eigenvalue (frequency) of a simply supported rectangular plate with linearly varying thickness are given for several taper ratios and plan geometries. These bounds were determined using a previously published method which yields convergent bounds. In the present study, all results have been obtained to within 0.5 percent maximum possible error.

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.

Vibrations of Rectangular Plates With Nonuniform Elastic Edge Supports

1980 ◽  
Vol 47 (4) ◽  
pp. 891-895 ◽  
Author(s):  
A. W. Leissa ◽  
P. A. A. Laura ◽  
R. H. Gutierrez
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Exact Solutions ◽  
Ritz Method ◽  
Equation Of Motion ◽  
The Other ◽  
Rectangular Plates ◽  
Governing Differential Equation ◽  
Vibration Problems ◽  
Elastic Edge

Two methods are introduced for the solution of free vibration problems of rectangular plates having nonuniform, elastic edge constraints, a class of problems having no previous solutions in the literature. One method uses exact solutions to the governing differential equation of motion, and the other is an extension of the Ritz method. Numerical results are presented for problems having parabolically varying rotational constraints.

scholarly journals Free vibration analysis of simply supported rectangular plates

2019 ◽  
Vol 29 ◽  
pp. 270-273
Author(s):  
Ganesh Naik Guguloth ◽  
Baij Nath Singh ◽  
Vinayak Ranjan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Simply Supported

scholarly journals LINEAR AND NONLINEAR FREE VIBRATION ANALYSIS OF RECTANGULAR PLATE

2021 ◽  
Vol 12 (1) ◽  
pp. 15-25
Author(s):  
Edward Adah ◽  
David Onwuka ◽  
Owus Ibearugbulem ◽  
Chinenye Okere
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Middle Surface ◽  
Rectangular Plates ◽  
Nonlinear Free Vibration ◽  
Surface Displacements ◽  
Linear And Nonlinear

The major assumption of the analysis of plates with large deflection is that the middle surface displacements are not zeros. The determination of the middle surface displacements, u0 and v0 along x- and y- axes respectively is the major challenge encountered in large deflection analysis of plate. Getting a closed-form solution to the long standing von Karman large deflection equations derived in 1910 have proven difficult over the years. The present work is aimed at deriving a new general linear and nonlinear free vibration equation for the analysis of thin rectangular plates. An elastic analysis approach is used. The new nonlinear strain displacement equations were substituted into the total potential energy functional equation of free vibration. This equation is minimized to obtain a new general equation for analyzing linear and nonlinear resonating frequencies of rectangular plates. This approach eliminates the use of Airy’s stress functions and the difficulties of solving von Karman's large deflection equations. A case study of a plate simply supported all-round (SSSS) is used to demonstrate the applicability of this equation. Both trigonometric and polynomial displacement shape functions were used to obtained specific equations for the SSSS plate. The numerical results for the coefficient of linear and nonlinear resonating frequencies obtained for these boundary conditions were 19.739 and 19.748 for trigonometric and polynomial displacement functions respectively. These values indicated a maximum percentage difference of 0.051% with those in the literature. It is observed that the resonating frequency increases as the ratio of out–of–plane displacement to the thickness of plate (w/t) increases. The conclusion is that this new approach is simple and the derived equation is adequate for predicting the linear and nonlinear resonating frequencies of a thin rectangular plate for various boundary conditions.

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