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

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.

Buckling of an Elliptical Plate With Simply Supported Edge Under Uniform Compression

1976 ◽  
Vol 43 (3) ◽  
pp. 455-458 ◽  
Author(s):  
Kenzo Sato
Keyword(s):  
Plate Theory ◽  
Mathieu Functions ◽  
Elliptical Plate ◽  
Buckling Mode ◽  
Uniform Compression ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Thin Plate Theory ◽  
The Stability ◽  
Circular Functions

On the basis of the ordinary thin plate theory, the stability of a simply supported elliptical plate subjected to uniform compression in its middle plane is considered by the use of circular functions, hyperbolic functions, Mathieu functions, and modified Mathieu functions which are solutions of the equilibrium equation of the buckled plate. The first five eigenvalues for the buckling mode symmetrical about both axes are calculated numerically for a variety of aspect ratios of the ellipse. The limiting cases of a circular plate and of an infinitely long strip are also discussed.

Simply-Supported Elliptical Auxetic Plates

2015 ◽  
Vol 32 (4) ◽  
pp. 413-419 ◽  
Author(s):  
T.-C. Lim
Keyword(s):  
Effective Stress ◽  
Principal Axis ◽  
Plate Material ◽  
Uniform Load ◽  
Elliptical Plate ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Principal Axes ◽  
Bending Stresses ◽  
Plate Center

AbstractWhile the maximum bending moment, and hence maximum bending stress, of a fully clamped elliptical plate under uniform load is independent from the Poisson's ratio of the plate material, the same cannot be said so when the plate is simply supported. This paper develops a simple but sufficiently accurate model for evaluating the bending stresses along the principal axes of a simply supported elliptical under uniform load. Plotted results suggest that bending stresses at plate center along the longer principal axis is minimized by the use of highly auxetic materials if the elliptical plate is almost circular but the use of mildly auxetic material is preferred if the aspect ratio of the elliptical plate is very high. Results also reveal that bending stresses at plate center along the shorter principal axis is minimized when the plate material is highly auxetic. Upon considering the von Mises stress state as the effective stress, it was found that the maximum effective stress is reduced with the use of auxetic and conventional materials for simply supported elliptical plates of low and high aspect ratios, respectively.

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

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.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

Free Vibration of Skew Laminates – A Brief Review and Some Benchmark Results

2019 ◽  
Vol 161 (A4) ◽  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Composite Laminates ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Static And Dynamic Analysis ◽  
Aspect Ratios ◽  
Skew Angles

This study investigates and reviews prior research works on skew composite laminates. The equivalent single layer theories are explored and discussed. An exhaustive review on static and dynamic analysis of composite skew laminates is also presented. Subsequently, a nine node isoparametric plate bending element is used for free vibration analysis of laminated composite skew plate with central skew cut out. The effect of shear deformation is incorporated in the formulation considering first order shear deformation theory. Two types of mass lumping schemes are analysed to study the effect of rotary inertia. Certain numerical examples of plates having different skew angles, skew cut out sizes, boundary conditions, thickness ratios (h/a), aspect ratios (a/b), fiber orientations and number of layers are solved which will be useful for benchmarking of future studies.

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