Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach

In this paper, the effect of mass diffusion in a thermoelastic nanoscale beam in context Lord and Shulman theory is studied. The analytical solution in the Laplace domain is obtained for lateral deflection, temperature, displacement, concentration, stress and chemical potential. The both ends of the nanoscale beam are simply supported. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. The results obtained are presented graphically for the effect of time and mass diffusion to display the phenomena physical meaning.