Comprehensive semi-analytical vibration analysis of rotating tapered AFG nanobeams based on nonlocal elasticity theory considering various boundary conditions via differential transformation method

Abstract

This paper is concerned with the vibration analysis of a rotating tapered axially functionally graded (AFG) nanobeam. The material properties of the nanobeam are assumed to vary along its length. Accordingly, Newtonian method is employed to derive the governing equation of the system considering Euler-Bernoulli beam assumptions. Also, the nonlocal elasticity theory (NET) is used in order to take the small scale effects into account in the modeling. In addition, the differential transformation method (DTM) is hired to solve the attained differential equation semi-analytically. Therefore, the obtained equations as well as boundary conditions are transformed into algebraic equations by the aid of DTM. Then, the characteristics equation can be solved to gain the non-dimensional frequencies of the system. After presenting the convergence and verification illustrations, some numerical results are discussed in detail to investigate the influences of various parameters namely nonlocal parameter, tapered ratio, angular velocity and FG index on the first three non-dimensional frequencies. As a principal result, it is disclosed that the nonlocal parameter shows both stiffness-hardening and stiffness-softening behavior in different bounds of the angular velocity. Totally, the numerical analysis reveals some important findings which are hoped to be used in efficient design of nano-structures benefited from the rotating nanobeams.