Free vibration of bi-directional functionally graded imperfect nanobeams under rotational velocity

Abstract

The prime objective of this study is allocated to comprehensive investigating the free vibration of bi-directional functionally graded (2D-FG) rotary nanobeam with even porosity distribution under different boundary conditions (BCs). The Material properties such as Young's modulus, mass density and nonlocal parameter are supposed to be graded in both axial and thickness directions according to the power-law distribution. The governing differential equations of nanobeam frequency response are derived by Hamilton principle together with the Euler-Bernoulli beam theory (EBT) and nonlocal elasticity theory (NET). A generalized differential quadrature method (GDQM) is developed for solving the eigenvalue problem. In the verification test, the excellent agreement between the presented results and those available in the literature is observed. Then, an exhaustive analysis is presented to investigate the influence of different parameters including variable nonlocal parameter, porosity index, axial functionally graded (AFG) index, conventional functionally graded (CFG) index and any existing BCs (Clamped-Clamped (C-C), Clamped-Simply (C-S), Clamped-Free (C-F) and Simply-Simply (S-S)) on the frequency response of rotary nanobeam. The numerical results demonstrate that by changing the mentioned parameters, the artificial pores have the hardening behavior in a special range of angular velocity and, it can be a major step in all further numerical and experimental investigations.