Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam

Abstract

Nano-structures such as carbon nanotube, nanobeams, nanorods, nanoplates, nanowires, and nanorings are tremendously used in various small-scale devices and investigating their dynamical behavior has been a hot research topic and can be beneficial in manufacturing and designing new devices. Therefore, free vibration analysis of a rotating cantilever double-tapered axially functionally graded material nanobeam is presented in this work. Due to the nano-scale dimension, classical beam theories are incompetent at describing the behavior of nanobeams. Thus, the nonlocal Eringen elasticity theory is adopted which considers the nonlocal scale effect for the small dimension effect of the structure of a nano-scale mechanism. The proposed nanobeam structure is assumed to taper linearly in two different axes, and its material is changing nonlinearly along its length. The equation of motion of the proposed system is found utilizing the nonlocal Eringen theory, and it is solved using a semi-analytical technique, differential transform method. Mode shapes and natural frequencies are extracted as the solution of the equation of motion of the system. Furthermore, the effects of several parameters such as nonlocal scale effect, rotational speed, hub radius, and taper ratios on the natural frequencies are investigated. Finally, a comparison between the presented work and other reported results show an excellent agreement.