Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

Abstract

In the present work, axial vibrational behavior of nanorods with different boundary conditions is researched. Bishop's rod theory is implemented to simulate the axial deflection. Size-dependency is captured by using Eringen's nonlocal elasticity theory. Based on nonlocal deformable boundary conditions and Stokes' transformation, a system of linear equations is derived and then constructed an Eigen value problem. Several numerical examples are presented to investigate the significance of various parameters such as geometric parameters, vibrational modes, various values of nonlocal parameter and axial spring parameters on the axial frequencies of nanorods. The numerical examples indicate that the deformable boundary conditions and small scale parameter have considerable effects on the axial vibration response.