The vibration of rectangular plates treated using simply supported plate functions in the Rayleigh—Ritz method

Abstract

The problem of the flexural vibration of rectangular plates has been treated extensively, with good result, using appropriate beam vibration mode shapes as admissible functions in both the Rayleigh and Rayleigh—Ritz methods [D. Young, J. Appl. Mech. 17, 448–453 (1950); G. B. Warburton, Proc. I. Mech. E. 168, 371–384 (1954); A. W. Leissa, J. Sound Vib. 31(3), 257–293 (1973); S. M. Dickinson, J. Sound Vib. 61(1), 1–8 (1978)]. An alternative set of admissible functions, derived from the mode shapes of vibration of plates having two parallel edges simply supported and boundary conditions on the other two edges appropriate for the plate under consideration, was suggested by Dickinson [J. Sound Vib. 59(1), 143–146 (1978)] and their use in Rayleigh's method demonstrated. The present paper describes the use of these functions in the Rayleigh—Ritz method and illustrates the improvement (or otherwise) in the natural frequencies so calculated over those obtained using beam functions for several example plates. It is found that for plates supported in some manner on all four edges, the simply supported plate functions yield superior results.