On the motion of thin plates and shells subject to Stokes damping

The motion of a homogeneous, thin rigid plate or shell subject to Stokes damping over its entire surface and to any additional system of workless forces, including those that are equipollent to zero, is studied. It is shown that the equation for the single-degree of freedom motion of every thin body having the same mass density per unit area is universal; the result, except for sufficient mathematical smoothness essential to integration over the body, is independent of any other physical features or dimensions of the body. A few examples illustrate the general problem and the universal nature of the equation of motion for thin plates and shells.