Mechanics of tapered AFG shear-deformable microbeams

In this paper, the forced nonlinear mechanics of axially functionally graded (AFG) microbeams is investigated based on a shear-deformable model and the modified couple stress theory. A tapered microbeam (a microbeam with varying width along the length) is considered. It is assumed that the material and geometrical properties of the microbeam are governed by nonlinear power law distributions along the length direction. Rotational and translational motions are formulated in Hamilton's framework and discretised with the aid of the Galerkin procedure. A continuation schemes is employed to find the nonlinear oscillation response of the tapered AFG shear-deformable microbeams clamped at both ends. The effects of material property distribution (i.e. the gradient index), and the small-size parameter on the nonlinear oscillations of the tapered AFG microbeams are discussed.