Transverse Vibration of Triangular Plates with Variable Thickness

ISSN： 0022-460X

Source： Journal of Sound and Vibration, Vol.194, Iss.4, 1996-07, pp. : 471-496

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Abstract

Transverse vibration of a triangular plate with thickness varying as a linear function of co-ordinates in the plane of the plate has been solved by working out several approximations in the Rayleigh-Ritz method. The basis functions are chosen so that the essential boundary conditions are satisfied. Three parameters control the three types of boundary conditions at the edges, two parameters control the thickness variation and two parameters control the shape of the plate. A general procedure has been laid down to compute the frequencies and the associated mode shapes for any set of these parameters. Convergence has been ensured by working out a sufficiently large number of approximations so that at least the first three frequencies converge to three significant digits. The results are tabulated for various values of the parameters and comparisons have been made with known results in special cases. Three-dimensional plots of the mode shapes have also been given in some cases.