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

Abstract

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.A list of symbols can be found on page 337.

New decay results in linear thermoelastodynamics

“…For each class, they introduce a family of appropriate surface integral measures, and finally, they combine the results obtained. Following Chiriţȃ and Ciarletta 14,20 and Chiriţȃ 19 important results have been obtained also for other types of materials (see also previous studies [21][22][23][24] and the references therein). In the context of the linear theory of elastodynamics for homogeneous and isotropic media, whose elasticity tensor is semi-strongly elliptic, Passarella 25 obtains results similar to those presented by Chiriţȃ and Ciarletta 14,20 but under different hypotheses; similar results are obtained by Tibullo 26 in the linear theory of porous elastic materials.…”

Rayleigh waves in isotropic strongly elliptic thermoelastic materials with microtemperatures

“…The ellipticity analysis is relevant in studying wave propagation [6] and has important applications in several contexts (e.g. [7][8][9][10][11][12][13][14]).…”

Shape memory and phase transitions for auxetic materials

“…Moreover, possible interactions between auxetic and composite (elastic and thermoelastic) materials have been investigated in , in the context of the study of spatial behavior of solutions. Transverse isotropy and rhombic materials also have been object of an intensive study with respect to the hypothesis of strong ellipticity of the elasticity tensor, closely related to the auxetic behavior of materials: at this regard, a detailed review (also concerning Mindlin‐type plates) can be found in and .…”