Surface energy-enriched gradient elastic Kirchhoff plate model and a novel weak-form solution scheme

In this work, we propose a non-classical Kirchhoff plate model to investigate surface energy and gradient elasticity effects on the static bending and free vibration behavior of micro-plates. Gurtin-Murdoch surface elasticity theory and a single-parameter gradient elasticity theory are combined to capture three types of size effects. The equations of motion and related boundary conditions of the model are obtained by the energy variational...