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1 International Journal of Applied Mechanics and Engineering

1 2006

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Free transverse vibrations of monoclinic rectangular plates with continuously varying thickness and density

Kumar Y., Tomar S. K.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 4

881-900

Free transverse vibrations of a rectangular plate composed of a monoclinic elastic material are discussed. The plate is considered to be exponentially varying in density and thickness along one direction of the plate. Hamilton's principle is used to derive the equation of motion and its solution is obtained using Chebyshev collocation technique. Frequency equations are derived for three boundary value problems when two edges of the plate are simply supported and the other two have different possibilities, namely (i) C - S - C - S (ii) C - S - S - S (iii) C - S - F - S, where C, S and F denote the clamped, simply supported and free edge respectively. Effects of thickness and density variation on modes of vibrations have been analyzed. Numerical computations have been performed for a specific model of monoclinic plates and the results obtained are compared with those for orthotropic plates already given in Lal (2003).