Flexural vibrations of rectangular plates with free edges (Q1819599)

In this paper, equations of flexural vibrations of isotropic, elastic plates, with rotatory inertia and shear deformation terms included, are solved for rectangular plates with all four edges free. The solutions are exact and in closed form. Two main restrictions apply: (1) the length/width ratio must be a ratio of integers; (2) for each value of Poisson's ratio, all the allowable modes must have the same frequency. In each case, that frequency lies between about 1.9 and 2.7 times the frequency, say \(\omega_ 0\), of the fundamental thickness-shear mode of the infinite plate. However, the equations, with the appropriate shear- correction factor, are intended for use at frequencies no higher than about \(1.2\omega_ 0\). To improve the accuracy at the higher frequencies, two additional correction factors are introduced to make the equations produce the exact values of frequency and wave-number, obtained from Rayleigh's exact dispersion relation, at the frequency and for the Poisson's ratio required by the solution for the rectangular plate.