A new Timoshenko beam model incorporating microstructure and surface energy effects

A new Timoshenko beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and complete boundary conditions for a Timoshenko beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface...