Sulla propagazione di onde termoclastiche in un mezzo omogeneo isotropo. Nota II

Agostinelli, Cataldo

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 50 (1971) no. 3, pp. 304-312.

Résumé

In a previous paper we have considered the propagation of thermoelastic waves in an homogeneous isotropic indefinite elastic medium, on the admission that in an assigned region of the medium act general body forces, and are distributed heating sources. Therefore we have exposed a procedure that reduces the determination of the displacement vector $\bf{u}$ of a point, and the temperature T, to the determination of two other vectors $\bf{u}_{1}$, $\bf{u}_{2}$, and a scalar function $\Psi$. The question simplifies itself in the remarkable case that the linear coefficient of the thermal expansion, as in general, is sufficiently small that we can neglect the terms which contain its square. In this case, by introduction of suitable potential functions, we have assigned the values of the vectors $\bf{u}_{1}$, $\bf{u}_{2}$ and the function $\Psi$. In this paper we assign now the explicit values of the displacement $\bf{u}$ in every point of the elastic medium, and of the temperature T. In particular we deduce the formulas relative to the case in which the region where act the body forces and are distributed the heating sources, vanishes around a point.