VIBRATIONS OF AN ANNULAR ISOTROPIC PLATE WITH ONE EDGE CLAMPED OR SIMPLY SUPPORTED AND AN INTERMEDIATE CONCENTRIC CIRCULAR SUPPORT

SummarySeveral plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

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On the Deflection of Rectangular Orthotropic Plates Under Lateral Loads

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100079906 ◽

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.

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Free Vibration Analysis of Thick Rectangular and Elliptical Plates with Concentric Cut-Out

Advances in Materials Science and Engineering ◽

10.1155/2021/7212075 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Anjibabu Merneedi ◽

Nalluri Mohan Rao ◽

L. Natrayan ◽

L. Yuvaraj ◽

Prabhu Paramasivam

Keyword(s):

Thick Plate ◽

Isotropic Plate ◽

Free Vibration Analysis ◽

Matching Condition ◽

High Accuracy ◽

Trigonometric Functions ◽

Elliptical Plate ◽

Inertia Effects ◽

Simply Supported ◽

Aspect Ratios

This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut-out in which geometries of plate and cut-outs are different, through a deflection matching condition by including shear deformation and rotary inertia effects, with less computational efforts and high accuracy. The modified Independent Coordinate Coupling Method (ICCM) is validated with FEM package (ANSYS) and applied to know the change in eigenvalues for a plate with cut-out by varying various parameters like aspect ratios, cut-out size, and thickness ratios. Trigonometric functions considered at the boundary level conditions of a simply supported plate should be satisfied. Free vibrational exploration on a thick isotropic plate with various aspect ratios and an elliptical plate with various sizes is carried out through the modified ICCM. Independent coordinates are applied for a plate domain and for a hole domain individually followed by equating the deflection condition of hole and plate, a reduced mass to express with cut-out from which eigenvalues can be obtained. The deflection matching condition facilitates the analysis even though the geometries of plate and cut-outs are different.

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Correlation Between some Stability Problems for Orthotropic and Isotropic Plates under Bi-Axial and Uni-Axial Direct Stress

Aeronautical Quarterly ◽

10.1017/s0001925900000809 ◽

1954 ◽

Vol 4 (1) ◽

pp. 83-92 ◽

Cited By ~ 29

Author(s):

W. H. Wittrick

Keyword(s):

Axial Compression ◽

Orthotropic Plate ◽

Isotropic Plate ◽

List Type ◽

Simply Supported ◽

Side Ratio ◽

Buckling Stress ◽

Isotropic Plates ◽

Stress Coefficient ◽

Rectangular Orthotropic Plate

SummaryFour buckling problems are considered, namely: — (a) A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides;(b) the same as (a) but with the ends clamped and sides simply supported;(c) a rectangular orthotropic plate, with the ends simply supported and sides clamped, subjected to compression on its ends; and(d) the same as (c) but with all edges clamped.In each case it is shown that the variables involved can all be combined into such a non-dimensional form that a single curve serves to give the value of the end compression required to cause buckling. This curve is identical with the curve of buckling stress coefficient against side ratio for a corresponding isotropic plate under uni-axial compression.

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Numerical Computation of First Three Frequencies for Circular Plate with Transcendental Thickness

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.f8112.038620 ◽

2020 ◽

Vol 8 (6) ◽

pp. 2304-2309

Keyword(s):

Circular Plate ◽

Isotropic Plate ◽

Ritz Method ◽

Thickness Variation ◽

Order Of Approximation ◽

Simply Supported ◽

Special Cases ◽

Different Types ◽

Important Approach ◽

Thickness Variations

In the present work, a very important approach Rayleigh-Ritz method has been used to compute the first few frequencies of a circular plate. The boundary conditions of circular plate are considered as a clamped and simply-supported. Different types of thickness variation of circular plate have been considered by researchers and a vast numbers of numerical results are available in the literature but none of the researchers consider the transcendental thickness variation which has been considered in the present work. The type of circular plate is considered as isotropic plate and significant numerical computations have been done for finding first three frequencies by varying the order of approximation and also the taper parameter. In special cases, results have been compared for uniform, linearly varying and transcendental thickness variations of circular plate and computed result are presented in the form of tables and graphs.

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Large-Deflection Theory for Plates With Small Initial Curvature Loaded in Edge Compression

Journal of Applied Mechanics ◽

10.1115/1.4010268 ◽

1951 ◽

Vol 18 (2) ◽

pp. 143-151

Author(s):

J. M. Coan

Keyword(s):

Stress Distribution ◽

Critical Load ◽

Flat Plate ◽

Large Deflection ◽

Isotropic Plate ◽

Transverse Stress ◽

Simply Supported ◽

Initial Curvature ◽

Deflection Theory ◽

Large Deflection Theory

Abstract This investigation of the buckling of a simply supported, rectangular isotropic plate with small initial curvature was undertaken to evaluate current procedures for deducing the true (flat plate) critical load from the measured deflections and strains of a nominally flat plate. The boundary conditions are those that are usually met in test practice but which have not been satisfied by earlier studies, i.e., stress-free supported edges and uniformly displaced loaded edges. Previous solutions require a distribution of transverse stress along the supported edges sufficient to keep them straight and parallel at all times. However, in most test specimens, the freedom of the supported edges to distort in the plane of the plate measurably influences the behavior of the plate and the stress distribution within it. Levy’s solution of von Kármán’s “large deflection” equations is adapted by the author to yield the nonuniform edge displacements that are characteristic of stress-free supported edges. Limited experimental evidence tends to confirm the predictions of this analysis.

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Semi-Analytical Solution Based on Strip Method for Buckling and Vibration of Isotropic Plate

Journal of Applied Mathematics ◽

10.1155/2013/796274 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10

Author(s):

Mohamed A. El-Sayad ◽

Ahmed M. Farag

Keyword(s):

Transition Matrix ◽

Isotropic Plate ◽

Mode Shapes ◽

Rectangular Plates ◽

Simply Supported ◽

Aspect Ratios ◽

Analytical Results ◽

Present Technique ◽

Benchmark Solutions ◽

Good Agreement

The present paper achieves a semianalytical solution for the buckling and vibration of isotropic rectangular plates. Two opposite edges of plate are simply supported and others are either free, simply supported, or clamped restrained against rotation. The general Levy type solution and strip technique are employed with transition matrix method to develop a semianalytical approach for analyzing the buckling and vibration of rectangular plates. The present analytical approach depends on reducing the strips number of the decomposed domain of plate without escaping the results accuracy. For this target, the transition matrix is expressed analytically as a series with sufficient truncation numbers. The effect of the uni-axial and bi-axial in-plane forces on the natural frequency parameters and mode shapes of restrained plate is studied. The critical buckling of rectangular plate under compressive in-plane forces is also examined. Analytical results of buckling loads and vibration frequencies are obtained for various types of boundary conditions. The influences of the aspect ratios, buckling forces, and coefficients of restraint on the buckling and vibration behavior of rectangular plates are investigated. The presented analytical results may serve as benchmark solutions for such plates. The convergence and efficiency of the present technique are demonstrated by several numerical examples compared with those available in the published literature. The results show fast convergence and stability in good agreement with compressions.

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Simply supported FPEDs connected by springs for broadband energy harvesting

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209323 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 201-210

Author(s):

Yoshikazu Tanaka ◽

Satoru Odake ◽

Jun Miyake ◽

Hidemi Mutsuda ◽

Atanas A. Popov ◽

...

Keyword(s):

Energy Harvesting ◽

Evaluation Method ◽

Energy Harvester ◽

Vibrational Energy ◽

Functional Materials ◽

Vibration Energy ◽

Theoretical Evaluation ◽

Vibration Energy Harvester ◽

Polyvinylidene Difluoride ◽

Simply Supported

Energy harvesting methods that use functional materials have attracted interest because they can take advantage of an abundant but underutilized energy source. Most vibration energy harvester designs operate most effectively around their resonant frequency. However, in practice, the frequency band for ambient vibrational energy is typically broad. The development of technologies for broadband energy harvesting is therefore desirable. The authors previously proposed an energy harvester, called a flexible piezoelectric device (FPED), that consists of a piezoelectric film (polyvinylidene difluoride) and a soft material, such as silicon rubber or polyethylene terephthalate. The authors also proposed a system based on FPEDs for broadband energy harvesting. The system consisted of cantilevered FPEDs, with each FPED connected via a spring. Simply supported FPEDs also have potential for broadband energy harvesting, and here, a theoretical evaluation method is proposed for such a system. Experiments are conducted to validate the derived model.

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