Sharif Digital Repository

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closedform... 

The geometrically nonlinear governing differential equations of motion and the corresponding boundary conditions are derived for the mechanical analysis of Timoshenko microbeams with large deflections, based on the strain gradient theory. The variational approach is employed to achieve the formulation. Hinged-hinged beams are considered as an important practical case, and their nonlinear static and free-vibration behaviors are investigated based on the derived formulation