The effect of pre-stress on the vibration and stability of elastic plates (Q1308907)

Plane incremental vibrations superimposed on the pure homogeneous deformation of a rectangular block of incompressible isotropic elastic material are studied in detail. Frequency equations, which determine the frequencies of symmetric and antisymmetric modes of vibration in terms of the underlying deformation and stress and of the in-plane aspect ratio of the block, are obtained in respect of a general form of strain-energy function. Different cases, dependent on the properties of the strain- energy function and on the deformation and stress, are enumerated; results analogous to those found in the (compressible) linear theory are recovered for comparison. The case of zero frequency is of special interest since the frequency equations then become bifurcation equations.