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Small Oscillations and Stability of a Thick Highly Elastic Slab

The problem of small oscillations of a thick slab superimposed on a finite biaxial deformation subject to both dead and hydrostatic lateral loads is investigated. A general frequency equation is derived from which specific results are deduced for both slender and stubby slabs. The question of the stability of a thick plate is studied with the aid of a kinetic stability criterion. The results for a special case are compared with others in the literature. Upon the introduction of certain effective Lamé moduli, correspondence with the work of others is established, and some existing discrepancies are explained. Some results for the disputed problem of stability in equibiaxial finite deformation are presented.