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. | Eigenvalue approach to nanoscale beam in modified couple stress thermo-elastic diffusion Engineering Solid Mechanics 2017 271-284 Contents lists available at GrowingScience Engineering Solid Mechanics homepage esm Eigenvalue approach to nanoscale beam in modified couple stress thermo-elastic diffusion Rajneesh Kumara and Shaloo Devib a Department of Mathematics Kurukshetra University Kurukshetra India b Department of Mathematics amp Statistics Himachal Pradesh University Shimla India A R T I C L EI N F O ABSTRACT Article history The problem of thermoelastic nanoscale beam based on a modified couple stress theory with Received 6 June 2017 diffusion subjected to ramp type heating is investigated. The Laplace transform technique and Accepted 7 September 2017 eigen value approach are applied to solve the equations which are written in the dimensionless Available online form. The expressions for displacement lateral deflection temperature change mass 7 September 2017 Keywords concentration axial stress and chemical potential are derived in the transformed domain. A Modified couple stress theory general algorithm of the inverse Laplace transform is developed to compute the results Thermoelastic diffusion numerically. The mathematical model is prepared for Copper material. The resulting quantities Nanoscale beam are depicted graphically to show the effects of time. Some particular cases of interest are also Laplace transform deduced from the present problem. Eigen value approach Ramp type heating 2017 Growing Science Ltd. All rights reserved. 1. Introduction Voigt 1887 was the first who introduced the concept of couple stress linear theory of elasticity and then this theories extended by Cosserat and Cosserat 1909 . Couple-stress theory is an extended continuum theory that includes the effects of a couple per unit area on a material volume in addition to the classical direct and shear forces per unit area. This immediately admits the possibility .
