Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory

In the present study, vibration response of non-homogenous and non-uniform microbeams is investigated in conjunction with Bernoulli–Euler beam and modified couple stress theory. The boundary conditions of the microbeam are considered as fixed at one end and free at the other end. It is taken into consideration that material properties and cross section of the microbeam vary continuously along the longitudinal direction. Rayleigh–Ritz solution method is utilized to obtain an approximate solution to the free transverse vibration problem. A detailed study is carried out to show the effects of material properties and taper ratios on natural frequencies of axially functionally graded tapered microbeams. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed between them.