On size-dependent vibration of rotary axially functionally graded microbeam

Study of the mechanical properties of axially functionally graded (AFG) microbeams is a challenging work due to the varying mechanical properties of these microbeams along the axis. In the present study, the transverse vibration of a rotary tapered AFG Euler–Bernoulli microbeam is studied based on the modified couple stress theory by considering the axial forces which are due to the rotation, in the form of true spatial variation. The governing equations and boundary conditions are derived according to the Hamilton's principle and the governing equations are solved with the aid of the generalized differential quadrature element method (GDQEM). The effects of the small-scale parameter, length and width of the beam, rate of cross-section change and nondimensional angular velocity on the vibration behavior of the non-uniform microbeam are studied for cantilever and propped cantilever boundary conditions. The vibrational behavior of AFG microbeam is also compared with pure metal and pure ceramic. The results are useful in designation of micromachines such as micromotors and micro-rotors.