Application of bi-directional functionally graded material model for free vibration analysis of rotating Euler-Bernoulli nanobeams

Document Type : Research Paper


Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran



In this work, mechanical vibration analysis of rotating bi-directional functionally graded Euler-Bernoulli nanobeams is investigated which has not been already studied deeply on the basis of latest authors’ knowledge. Material properties vary along the thickness and axis directions based on power-law distribution. The nonlocal elasticity theory of Eringen (NET) is utilized for modeling of small-scale effects. Different boundary conditions are considered as clamped-clamped (C-C), clamped-simply (C-S) and clamped-free (C-F). Governing equations and associated boundary conditions are derived based on minimum total potential energy and the generalized differential quadrature (GDQ) method is employed for the solution process. Convergence and verification studies are accomplished for affirmation of this work and in the continuation, the effects of various parameters namely hub ratio, rotation speed and power indexes along x and z directions on the dimensionless natural frequencies are investigated. It is revealed that the decrement made by the different value of n_x in the natural frequency parameter is more effective than the reduction caused by the n_z, especially for the higher rotation speed.