Over the years, many different plate theories and models have been employed to rnodel various different effectç of interest in the andysis of stationary (non-rotat ing) plates.
However, in the realm of thin plates, two plate theories have established themselves
as basic tools in the literature. These are the Kirchhoff and von Karman models of a plate. These models use the same fundamental assumptions. The difference between them lies in the choice of strain-displacement relations. The Kirchhoff theory uses linear strain-displacement relations. This amounts to assurning infinitesimal displacements and results in a linear theory. The Von Karman theory diEers in that nonlinear transverse displacement terms are retained in the st rain-displacement equat ions. This removes the assumption of small transverse displacements, resulting in a nonlinear disk model. Hence, to develop a mode1 for a spinning disk, the simplest approach is to choose the appropriate plate or membrane representation and then to incorporate the ~ffectof the rotation. It is thus no surprise that this is the approach that has been foilowed in the existing literature. However, the exact manner in which the effect of the spin is incorporated into the equations of motion and corresponding boundary conditions leads to different equations with different solutions and techniques required to obtain those
solutions. Most of the investigations on spinning disks have focused on andysis using linear plate or membrane theory. .halysis of spinning disks using nonlinear theories has rarely been discussed in the Ăźterature. Linear theories can be adequately used to represent the dynamics of a thin plate only when the transverse deflections of the plate are much smaller than the thickness of the plate. For very thin plates, the transverse defiections can easily become larger than the thickness of the plate, rendering the linear plate theory