Before revision: This paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and viscoelastic effects . First, by the C0-semigroup theory, we prove the well posedness of the considered problemwith Dirichlet boundary conditions. An exponential decay is obtained by construction of the Lyuponov functional. Finally, a numerical study is done based on P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization , where we study the stability of the scheme, analysis of the error and obtained some numerical simulations  .
After revision: This paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem under an unusual assumption, and by using a multiplier technique in two different cases, with frictional damping in the angular rotation and with frictional damping in the vertical displacement. In numerical parts, we first obtained a numerical scheme for problem by P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization , where we study the stability of the scheme, analysis of the error and obtained some numerical simulations .