STABILITY AND VIBRATION OF PRESTRESSED COMPRESSIBLE ELASTIC PLATES

In a recent paper [1], Ogden and Roxburgh Int. J. Engng Sci. have give n a detailed account of plane incremental vibrations of a rectangular plate of incompressible isotropic elastic material subject to an under lying homogeneous pure strain. In this paper corresponding results in respect of a compressible elastic material are derived. Specifically, for a general form of strain-energy function, equations governing the frequency of symmetric and antisymmetric modes of vibration are obtain ed. Depending on the form of strain-energy function, the underlying st ate of deformation and the aspect ratio of the plate, nine distinct ca ses arise together with several subcases. This is similar to the situa tion in the incompressible theory, although, for compressible material s, additional subcases appear. The emergence of quasi-static modes of deformation, corresponding to zero frequency, is accorded special atte ntion since the frequency equations then reduce to bifurcation equatio ns, which provide information about the boundary of stability of the u nderlying configuration in deformation space. Stability criteria are a nalysed in detail for a general form of strain-energy function. The dy namic and static results are illustrated by numerical calculations for a number of simple strain-energy functions.