application of bi-directional functionally graded material model for free vibration analysis of rotating euler-bernoulli nanobeams

In this work, mechanical vibration analysis of rotating bi-directional functionally graded euler-bernoulli nanobeams is investigated, which has not already been studied deeply based on the 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 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 to affirm 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 values of 𝑛𝑥 in the natural frequency, parameter is more effective than the reduction caused by the 𝑛𝑧, especially for the higher rotation speed.