Influence of Chebyshev Collocation Points on the Convergence of Results in the Analysis of Annular Plate Vibrations

R. P. Singh; S. K. Jain

doi:10.6180/jase.2005.8.1.07

Influence of Chebyshev Collocation Points on the Convergence of Results in the Analysis of Annular Plate Vibrations

R. P. Singh This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and S. K. Jain²

¹Department of Applied Mechanics, Birla Institute of Technology Mesra, Ranchi835215, India
²Department of Applied Mathematics, Birla Institute of Technology Mesra, Ranchi835215, India

Received: February 11, 2004
Accepted: August 17, 2004
Publication Date: March 1, 2005

Download Citation: ||https://doi.org/10.6180/jase.2005.8.1.07

ABSTRACT

The Chebyshev collocation points have been used as the interpolating nodes in the analysis of vibrations ofan annular plate by an interpolation approximation and their influence on the convergence of the results has been investigated. For the purpose, two different interpolating approximate methods - the spline and the collocation - have been considered and, for a typical value of the plate parameters and boundary conditions in each one, the frequency parameters of the plate have been computed by taking both the equi-spaced nodes as well as the Chebyshev points as the interpolating nodes. A faster rate of convergence and appreciably improved results have been obtained at Chebyshev collocation points as compared to the results obtained at equi-spaced nodes (Fourier points) in each of the methods for the lower values of radii ratio. However, no appreciable influence of the Chebyshev collocation points on the results has been observed for the higher values of the radii ratio in any of the methods.

Keywords: Chebyshev Points, Annular Points, Interpolation Approximation, Spline and Collocation Methods, Radii Ratio

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