Decay properties of solutions of a Mindlin-type plate model for rhombic systems

In the present paper, we investigate the spatial behavior of transient and steady-state solutions for the problem of bending applied to a linear Mindlin-type plate model; the plate is supposed to be made of a material characterized by rhombic isotropy, with the elasticity tensor satisfying the strong ellipticity condition. First, using an appropriate family of measures, we show that the transient solution vanishes at distances greater than cT from the support of the given data on the time interval [0,T], where c is a characteristic material constant. For distances from the support less than cT, we obtain a spatial decay estimate of Saint-Venant type. Then, for a plate whose middle section is modelled as a (bounded or semiinfinite) strip, a family of measures is used to obtain an estimate describing the spatial behavior of the amplitude of harmonic vibrations, provided that the frequency is lower than a critical value.