A theoretical analysis of the free vibrations of a clamped circular plate with damping

A theoretical analysis of the free vibrations of a clamped circular plate was undertaken. The effects of transverse shear were considered for application to relatively thick plates in which there exist sharp transients and frequencies corresponding to higher modes. The method adopted by R. D. Mindlin was used to develope [sic] the differential equation of motion for the plate. The damping effect due to the resistance of the medium in which the plate vibrates was also considered. This damping was assumed to be due to the generation of pressure waves caused by the displacement of the plate...Since the solution requires that the initial displacement function be known, the example presented is at best an approximation because the initial displacement function assumed did not include shear deformation. It should be emphasized that only one possibility of the roots of the frequency equation has been discussed in this investigation. Therefore, the solution presented is a particular solution. However, it is hoped that this is a significant first step in the study of the stated problem --Abstract, page ii-iii