Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material

Abstract

The elastic spring boundary conditions play an important role in dynamical analysis of functionally graded (FG) nanorods. However, these special issues have not been properly paid attention to in the previously developed non-local models. In this work, longitudinal vibration analysis of FG restrained nanorods is presented via non-local elasticity theory. Two axial springs are attached to a FG nanorod at both ends. By considering the non-local differential relations for the FG nanorod, a coefficient matrix is derived and analysed via an exact eigenvalue method. Finally, the results calculated from finite-element method are used to validate the present method. The influence of FG index, non-local parameter and boundary conditions on the axial frequencies of FG nanorods is discussed.