Coupling effects of surface energy, strain gradient, and inertia gradient on the vibration behavior of small-scale beams

This paper develops three surface energy-enriched gradient elastic beam models, respectively, in the contexts of Euler-Bernoulli, Timoshenko, and Levinson-Brickford-Reddy kinematic hypotheses to investigate the coupling effects of surface energy, strain gradient, and inertia gradient on the vibration behavior of small-scale beams. Modified strain-inertia gradient elasticity theory and Gurtin-Murdoch surface elasticity theory are combined to...