Axial vibration analysis of cracked nanorods with arbitrary boundary conditions

The axial vibration of cracked nanorods (carbon nanotubes) with arbitrary boundary conditions is studied. The nonlocal elasticity theory is used, and the crack severity is modeled by an axial spring representing the discontinuity in the axial displacement. The present model is set up by dividing the nanorod into two segments connected by an axial spring located at the cracked section. The axial displacement functions are sought as the combination of two Fourier sine series and Stokes’ transformation. Vibration frequencies of a nanorod for variant crack positions under different boundary conditions are calculated by means of the proposed method. The purpose of this study is mainly to present a general analytical method for the dynamical analysis of cracked nanorods with arbitrary boundary conditions (rigid or restrained) rather than to investigate a specific problem