Displacements in a polar-orthotropic disk of varying thickness

1963 ◽  
Vol 14 (2) ◽  
pp. 101-111 ◽  
Author(s):  
Charles W. Bert
Keyword(s):  
Varying Thickness ◽  
Orthotropic Disk ◽  
Polar Orthotropic

STRETCHING OF A POLAR-ORTHOTROPIC DISK OF VARYING THICKNESS UNDER ARBITRARY BODY FORCES

AIAA Journal ◽  
1963 ◽  
Vol 1 (6) ◽  
pp. 1385-1390 ◽  
Author(s):  
CHARLES W. BERT ◽  
FRANCIS W. NIEDENFUHR
Keyword(s):  
Varying Thickness ◽  
Body Forces ◽  
Arbitrary Body ◽  
Orthotropic Disk ◽  
Polar Orthotropic

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.

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.

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