Free vibration characteristics of rectangular cantilever plates.

As a step in the determination of the dynamic characteristics of missile fins, the frequencies and mode configurations of free vibration of uniform rectangular plates fixed along one edge are obtained for various (1/2, 1, 2, 5) cantilever span to chord ratios. Equations are set up in terms of influence coefficients and solved by matrix iteration. The Ritz method is also used in which the plate energies are expressed in terms of beam functions corresponding to the normal modes of vibration of uniform beams. It is shown that the first plate bending (symmetric) frequency corresponds closely to that of a uniform cantilever beam modified to account for the plate flexural rigidity factor. The first torsional (antisymmetric) frequency varies almost linearly with plate length to breadth ratio. An empirical equation is developed for ease in determination of this frequency. Experimental spot checks on a square cantilever plate indicate agreement within 2 percent of theoretical values for the first two frequencies. (Author).