Free Asymmetric Transverse Vibration of Parabolically Varying Thickness Polar Orthotropic Annular Plate with Flexible Edge Conditions

R.P. Singh; S.K. Jain

doi:10.6180/jase.2004.7.1.07

Free Asymmetric Transverse Vibration of Parabolically Varying Thickness Polar Orthotropic Annular Plate with Flexible Edge Conditions

R. P. Singh ¹ and S. K. Jain²

¹Department of Applied Mechanics Birla Institute Technology Mesra, Ranchi−835215, India
²Department of Applied Mathematics Birla Institute Technology Mesra, Ranchi−835215, India

Received: June 14, 2003
Accepted: October 24, 2003
Publication Date: March 1, 2004

Download Citation: ||https://doi.org/10.6180/jase.2004.7.1.07

ABSTRACT

Free asymmetric transverse vibration of a polar orthotropic thin annular plate with parabolically varying thickness in radial direction have been computed on the basis of classical plate theory considering both the peripheries of the plate elastically restrained against translation and rotation. The fourth order linear differential equation with variable coefficients governing the motion in the present study has been solved using collocation interpolation technique taking Chebyshev points as the interpolating nodes. Frequency parameters of the plate considering some typical values of taper parameters, rigidity ratios and the radii ratios have been presented for the first three modes of vibration.

Keywords: Asymmetric Vibrations, Polar Orthotropic Annular Plate, Parabolically Varying Thickness, Chebyshev Points, Edges Elastically Restrained Against Translation and Rotation

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