Nonlocal Timoshenko frequency analysis of single-walled carbon nanotube with attached mass: An alternative hamiltonian approach

In the present paper, the nonlocal vibration analysis of single-walled carbon nanotube as nanosized mass-sensor is examined. The nanotube is modeled as a clamped-free Timoshenko beam carrying an attached mass at its free end. Using the nonlocal Timoshenko beam theory, a re-formulation of Hamilton's principle has been presented and the equations of motion and the general corresponding boundary conditions have been derived. The main purpose of this paper is to show the sensitivity of the nanotube to the values of added mass and the in presence of nonlocal parameter on the fundamental frequencies values. Some numerical examples have been performed and discussed and the obtained results are compared with those of available works in literature and listed in bibliography.