Variational method for non-conservative instability of a cantilever SWCNT in the presence of variable mass or crack

Abstract

In the present paper the non-conservative instability of a cantilever single- walled carbon nanotube (SWCNT) through nonlocal theory is investigated. The nanotube is modeled as clamped-free beam carrying a concentrated mass, located at a generic position, or in presence of a crack, and subjected to an axial load, at the free end. Nonlocal Euler-Bernoulli beam theory is used in the formulation and the governing equations of motion and the cor- responding boundary conditions are derived using an extendend Hamilton's variational principle. The governing equations are solved analitically. In or- der to show the sensitivity of the SWCNT to the values of an added mass, or crack and the in uence of the nonlocal parameter and nondimensional crack severity coe cient on the fundamental frequencies values, some nu- merical examples have been performed and discussed. Also, the validity and the accuracy of the proposed analysis have been con rmed by comparing the results with those obtained from the literature.