On a structural acoustic model which incorporates shear and thermal effects in the structural component

In this paper we consider a structural acoustic model which takes account of thermal effects over and above displacement, rotational inertia and shear effects in the flat flexible structural component of the model. Thus the structural medium is a Reissner-Mindlin plate into which an additional degree of freedom, viz. temperature variation in the plate, has been introduced and the constitutive equations for the structural acoustic model couple parabolic dynamics with hyperbolic dynamics. We show unique solvability of the mathematical model and investigate the effect of the presence of thermal effects on the mechanical dissipation devices needed to attain uniform stabilization of the two-dimensional model in which the structural component is a Timoshenko beam. It turns out that, as in linear structural acoustic models which use the Euler-Bernoulli equation or the Kirchoff equation to describe the deflections of the thermo-elastic structural medium, uniform stabilization of the energy associated with the model can be attained without introducing mechanical dissipation at the free edge of the beam. Open problems with regard to the stabilization of the three-dimensional model are outlined.