Dynamic Behavior of Atomic Force Microscope Cantilevers

The linear and non-linear dynamic behavior of rectangular, double tapered, dagger shaped and V shaped atomic force microscope cantilevers in contact mode have been investigated. In this work all necessary details such as cantilever thickness and normal and lateral contact stiffness have been considered. The differential equations of motion has been solve by the exact solution for the rectangular cantilever, but for the double tapered, dagger shaped and V shaped AFM cantilevers the complexity of the governing equations and boundary conditions precludes modeling using closed-form expressions, thus the numerical solutions has been applied. On the other hand, naturally Tip-Sample interaction force is non-linear. Hertzian contact theory has been applied for non-linear Tip-Sample interaction force. In the linear analysis the effects of above details on the resonant frequency and sensitivity to the normal contact stiffness has been studied. In the non-linear analysis, we have studied the effects of different parameters on the non-linear dynamic behavior of the system and suggested approximated areas for applying linear Tip-Sample interaction model instead of non-linear model.