Shenjie Zhou

TL;DR: In this article, the dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of modified couple stress theory and Hamilton's principle, and the difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.

TL;DR: In this paper, the static and dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of strain gradient elasticity theory due to Lam et al.

TL;DR: In this article, a micro scale Timoshenko beam model based on strain gradient elasticity theory was developed and the governing equations, initial conditions and boundary conditions were derived simultaneously by using Hamilton's principle.

TL;DR: In this article, a size-dependent Kirchhoff micro-plate model was developed based on the strain gradient elasticity theory, which contains three material length scale parameters, which may effectively capture the size effect.

TL;DR: In this paper, the nonlinear governing equation of microbeam based on the strain gradient theory is derived by using a combination of the strain gradients theory and the Hamilton's principle, and the non-linear static bending deformation, the post-bucking problem and nonlinear free vibration are analyzed.