Eigenvalue approach to nanoscale beam in modified couple stress thermo-elastic diffusion

Abstract

The problem of thermoelastic nanoscale beam based on a modified couple stress theory with diffusion subjected to ramp type heating is investigated. The Laplace transform technique and eigen value approach are applied to solve the equations which are written in the dimensionless form. The expressions for displacement, lateral deflection, temperature change, mass concentration, axial stress and chemical potential are derived in the transformed domain. A general algorithm of the inverse Laplace transform is developed to compute the results numerically. The mathematical model is prepared for Copper material. The resulting quantities are depicted graphically to show the effects of time. Some particular cases of interest are also deduced from the present problem.