scholarly journals Asymmetric Vibration of Polar Orthotropic Annular Circular Plates of Quadratically Varying Thickness with Same Boundary Conditions

2008 ◽  
Vol 15 (6) ◽  
pp. 599-617 ◽  
Author(s):  
N. Bhardwaj ◽  
A.P. Gupta ◽  
K.K. Choong
Keyword(s):  
Ritz Method ◽  
Plate Thickness ◽  
Thickness Variation ◽  
Lateral Vibration ◽  
Circular Plates ◽  
Thickness Profile ◽  
Varying Thickness ◽  
Winkler Elastic Foundation ◽  
Polar Orthotropic ◽  
Asymmetric Vibration

In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a) higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b) Lateral vibration characteristics ofF-Fplatesis more sensitive towards parametric changes in material orthotropy and foundation stiffness thanC-CandS-Splates; (c) Effect of quadratical thickness variation on fundamental frequency is more significant in cases ofC-CandS-S platesthan that ofF-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d) Fundamental mode of vibration ofC-CandS-Splatesis axisymmetrical while that ofF-Fplatesis asymmetrical.

AXISYMMETRIC VIBRATION OF POLAR ORTHOTROPIC CIRCULAR PLATES OF QUADRATICALLY VARYING THICKNESS RESTING ON ELASTIC FOUNDATION

2005 ◽  
Vol 05 (03) ◽  
pp. 387-408 ◽  
Author(s):  
N. BHARDWAJ ◽  
A. P. GUPTA
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Three Dimensional ◽  
Normal Modes ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Varying Thickness ◽  
Edge Conditions ◽  
Polar Orthotropic

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

Finite Element Analysis of the Lateral Vibration of Thin Annular and Circular Plates With Variable Thickness

1998 ◽  
Vol 120 (3) ◽  
pp. 747-752 ◽  
Author(s):  
Dian-Yun Chen ◽  
Bao-Sheng Ren
Keyword(s):  
Finite Element Analysis ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Thickness ◽  
Mode Shapes ◽  
Lateral Vibration ◽  
Circular Plates ◽  
Element Analysis ◽  
Numerical Convergence ◽  
Polar Orthotropic

The method of annular finite elements with variable thickness is applied for analyzing the lateral vibration of thin annular and circular plates. The material of the plates may be of isotropic or polar orthotropic and the plate thickness may vary arbitrarily with the radius. Natural frequencies and mode shapes of the axisymmetric and nonaxi-symmetric modes are obtained. The numerical convergence of the method has been tested and comparisons have been made with the results obtained in other studies. It has been proved that the convergence of this method is very rapid and obtained results are very accurate.

scholarly journals Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations

2008 ◽  
Vol 15 (6) ◽  
pp. 713-723 ◽  
Author(s):  
A.K. Gupta ◽  
Anupam Khanna
Keyword(s):  
Rectangular Plate ◽  
Nuclear Reactor ◽  
Ritz Method ◽  
Cartesian Product ◽  
Frequency Equation ◽  
Elastic Behavior ◽  
Thickness Variation ◽  
Engineering Structures ◽  
Varying Thickness ◽  
Elastic Rectangular Plate

Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

scholarly journals Transverse Vibrations of Clamped and Simply-Supported Circular Plates with Two Dimensional Thickness Variation

2012 ◽  
Vol 19 (3) ◽  
pp. 273-285 ◽  
Author(s):  
N. Bhardwaj ◽  
A.P. Gupta ◽  
K.K. Choong ◽  
C.M. Wang ◽  
Hiroshi Ohmori
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Two Dimensional ◽  
Circular Plates ◽  
Simply Supported ◽  
Modes Of Vibration ◽  
Dimensional Boundary ◽  
Special Case

Two dimensional boundary characteristic orthonormal polynomials are used in the Ritz method for the vibration analysis of clamped and simply-supported circular plates of varying thickness. The thickness variation in the radial direction is linear whereas in the circumferential direction the thickness varies according to coskθ, wherekis an integer. In order to verify the validity, convergence and accuracy of the results, comparison studies are made against existing results for the special case of linearly tapered thickness plates. Variations in frequencies for the first six normal modes of vibration and mode shapes for various taper parameters are presented.

Vibration of Nonhomogeneous Orthotropic Elliptic and Circular Plates With Variable Thickness

2006 ◽  
Vol 129 (2) ◽  
pp. 256-259 ◽  
Author(s):  
S. Chakraverty ◽  
Ragini Jindal ◽  
V. K. Agarwal
Keyword(s):  
Variable Thickness ◽  
Ritz Method ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Material ◽  
Orthotropic Plates ◽  
Various Boundary Conditions ◽  
Vibrational Characteristics ◽  
Schmidt Orthogonalization ◽  
Orthogonalization Procedure

In this paper, study of nonhomogeneity as well as variable thickness in elliptic and circular orthotropic plates is undertaken. Nonhomogeneity of plate material is assumed to be a quadratic variation of Young’s modulii and density whereas shear modulus, is considered to vary linearly along both the axes. The quadratic thickness variation in orthotropic nonhomogeneous plates is also considered. Effect of variation of these parameters on vibrational characteristics are analyzed for various boundary conditions at the edges. Results are obtained using boundary characteristic orthogonal polynomials generated by using Gram-Schmidt orthogonalization procedure in Rayleigh-Ritz method.

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