Spatial estimates concerning the harmonic vibrations in rectangular plates with voids

Abstract

This paper studies the spatial behaviour of the amplitude of a harmonic vibration in a rectangular plate of Mindlin type, made of a homogeneous and isotropic elastic material with voids. Provided the frequency of vibration is lower than the critical value, some appropriate measures are introduced relating the amplitude of resulting harmonic vibration, and the corresponding first-order differential inequalities are established under mild conditions on the elastic coefficients. The case of a semi-infinite plate is also studied and some Phragmén–Lindelöf alternatives are established.