Vibrations and Stability of Plates under Initial Stress

A linear theory of the motion of elastic plates is established which, in addition to initial membrane forces, takes into account initial moments and transverse shear forces. The equations of motion are obtained by linearizing the appropriate nonlinear plate equations and, in the absence of initial stresses, they are reduced, depending on the order of approximation, to either the classical (elementary) or the Mindlin plate theory (classical theory extended to include the effects of transverse shear deformation and rotatory inertia). These equations are applied to the solution of particular problems and the effect of uniform initial compression, bending moment and transverse shear force on the frequencies of the flexural , longitudinal, thickness-shear and the first two face-shear modes is discussed.