Dynamic Modeling and Vibration Analysis of the Atomic Force Microscope

The objective of this paper is to formulate the equations of motion and to investigate the vibrations of the atomic force microscope (AFM), which is divided into the contact and noncontact types. First, the governing equations of the AFM including both base oscillator and piezoelectric actuator are obtained using Hamilton’s principle. In the dynamic analysis, the piezoelectric layer is treated as a sensor to measure the deflection and as an actuator to excite the AFM via an external voltage. The repulsive force and van der Waals (vdW) force are considered in the contact and noncontact types of the AFM, respectively. Some important observations are made from the governing equations and boundary conditions. Finally, numerical results using a finite element method are provided to illustrate the excitation effects of base oscillator and piezoelectric actuator on the dynamic responses.