Dynamic Behavior Analysis of Atomic Force Microscope Based on Gradient Theory

In this paper, the dynamic behavior of atomic force microscope (AFM) based on non-classical strain gradient theory was analyzed. For this aim atomic force microscope micro-beam with attached tip has been modeled as a lumped mass. Micro-beam has stimulated via a piezoelectric element attached to the end of clamped and non-linear partial differential equation of the system has extracted based on Euler-Bernoulli theory and to be converted into ordinary differential equation by using Galerkin and separation method. The classic continuum theory because of lack of consideration size effect that has been observed in many experimental studies, has little accuracy in predicting the mechanical behavior of Nano devices. In this study, the stability region of micro-beam are determined analytically and validated by comparison with numerical results. Difference between presented analysis in dynamic behavior of micro-beam by classic and non-classic theories has been shown with variety of diagrams. It is clear that consideration the size effect changes the dynamical behavior of the problem completely and it is possible while classical theory predicts stable behavior for microscope the size effect is caused bi-stability. The results in this paper are very useful for the design and analysis of atomic force microscope.