The study of the transverse vibrations of rectangular plates is among the most widely studied topics in structural dynamics, and the application of the assumed modes/Rayleigh-Ritz method to derive models of this vibration for various sets of boundary conditions has been employed for nearly the entire century. The shape functions employed in the assumed modes method need not be eigenfunctions of the governing equations of motion, but instead must form an admissible set, in part by satisfying the geometric boundary conditions of the system, as shown by Meirovitch [1]. Given the extreme difficulty in solving for closed form, analytic solutions to the plate vibration equations, study of these vibrations has often relied upon admissible function sets taken from other sources. In particular, for free vibration of a beam, closed form solutions are easily written for multiple boundary condition pairs, and such solutions are often employed as admissible sets in the rectangular plate vibration problem. Specifically, shape functions satisfying similar beam boundary conditions have been employed in the assumed modes method for rectangular plates by Leissa [2,3], Warburton [4] and Young [5]. Relatively recently, Bhat and Mundkur [6] offered an excellent collection of natural frequencies of the freely vibrating plate. These frequencies were obtained by using ''plate characteristic functions'' obtained from reduction of the plate vibration equations in the Rayleigh-Ritz method. Specifically, Bhat and Mundkur offer the first 36 frequencies for 11 cases, with variation of plate aspect ratio and boundary conditions. They demonstrate the validity of the plate functions by comparing the frequencies generated by the plate functions with previously published data. However, in the results presented for asymmetric plates, several vibration modes/frequencies were omitted from the sorted sets tabulated. As such, data presented herein are intended to supplement the work of Bhat and Mundkur [6], tabulating modal indices and natural frequencies for omitted modes.
2.
The authors have constructed a numerical method for implementing the assumed modes/Rayleigh-Ritz method for the rectangular plate, employing as assumed modes a set of beam functions, as first presented by Warburton [4] and later by Blevins [7]. (Note that separate beam functions are used in each of the plate's two directions, and the convolution of the two, according to principles of 0022-460X/98/430579