Abstract
Taking the von Kármán geometrically nonlinearity into account, this paper presents a nonlinear finite element formulation of axially functionally graded(AFG) tapered microbeams, which is based on the modified couple stress and Euler–Bernoulli beam theory. The profiles of physical parameters such as elasticity modulus and mass density of the microbeam are assumed to be a simple power-law form along the length direction, while either width or height of the beam changes linearly in axial direction. The size-dependent nonlinear free vibration of AFG non-uniform microbeams is analyzed by using finite element simulation. The correctness of the present analysis is validated by comparing computed results with those available for AFG tapered beams. The effects of vibration amplitude, variation of the taper ratio in cross section and gradient index of material along the length and material length scale parameter as well as boundary conditions on nonlinear fundamental frequency are discussed.
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