Free axial vibration analysis of axially functionally graded thick nanorods using nonlocal Bishop's theory

Abstract

Free axial vibration of axially functionally graded (AFG) nanorods is studied by focusing on the inertia of lateral motions and shear stiffness effects. To this end, Bishop's theory considering the inertia of the lateral motions and shear stiffness effects and the nonlocal theory considering the small scale effect are used. The material properties are assumed to change continuously through the length of the AFG nanorod according to a power-law distribution. Then, nonlocal governing equation of motion and boundary conditions are derived by implementing the Hamilton's principle. The governing equation is solved using the harmonic differential quadrature method (HDQM), After that, the first five axial natural frequencies of the AFG nanorod with clamped-clamped end condition are obtained. In the next step, effects of various parameters like the length of the AFG nanorod, the diameter of the AFG nanorod, material properties, and the nonlocal parameter value on natural frequencies are investigated. Results of the present study can be useful in more accurate design of nano-electro-mechanical systems in which nanotubes are used.