Free Waves in Incoherent Slabs

Abstract

Standard plate theories [6-9] deal with coherent plates, that is to say, plates made of a linearly elastic material which (either is isotropic or) has a preferred response axis c parallel to the normal z to the plate’s cross section: typically, the material is transversely isotropic with respect to c, or monoclinic with respect to a plane nor-mal to c, and is so arranged in the plate that c × z = 0 . Incoherent plates are those for which sin θ = ∣c × z∣ ∈ ]0,1[ . Incoherence — the smallest amount of it — destroys the prime source of simplicity of classical plate theories, i.e., the orthogonality in energy of the membrane and flexure regimes.