Smart cantilever beams for nanomanipulation

A smart micro cantilever beam, consisting of an atomic force microscope probe bonded with a piezoelectric actuator, is proposed to enhance the ability of mechanical nanomanipulation. A precise three-section Euler-Bernoulli beam model is developed to describe the dynamics of the beam. The forced vibration solution of this model with respect to two independent inputs from the piezoelectric actuator and the base excitation is derived. Through the solution and the geometry relationship, the trajectory of the end of the tip is obtained from the motion of the free end of the AFM probe. Based on the resonant response from two harmonic inputs, nano-scale elliptical and linear tip trajectories are predicted at the second dynamic mode. Analytical and numerical studies show that the characteristics of the resulting trajectories are influenced by the magnitudes of the two inputs. The potential applications of the elliptical and linear trajectories for nanomanipulation are proposed