Modelling of Non-Uniform Piezoelectric Micro-Cantilever in Different Environments

Abstract

In recent years, Atomic Force Microscopy (AFM) has been known as a powerful and efficient tool for surface imaging in different environment. To enhance image quality and more precise prediction of Micro-cantilever (MC) behaviour, accuracy in the MC modeling and simulation and detecting the MC sensitivity to geometric parameters has great importance. To model the vibration motion of the AFM non-uniform piezoelectric MC, Timoshenko beam theory is used in order to consider the effect of shear effect in air and liquid environment. In addition, the effect of the forces imposed by the ambient and sample surface is considered. Frequency response has been studied in the air and different liquid environments and the obtained results have been compared with experiential results as well as with results obtained from Euler-Bernoulli beam theory that is reflective of higher precision exercised in the modeling in respect to Euler-Bernoulli beam theory. Efast statistical method, which is found efficient and quick in the survey of linear and nonlinear models and takes the inter-parameter coupling effect into consideration besides calculating the sensitivities unique to each of the factors, has been applied in order to analyse the geometrical parameters' effects on the MC natural frequencies in the air and water environments.