Sensitivity Analysis of the Non-Linear Deflection of Non-Straight AFM Micro-Cantilever

Atomic force microscopy represents a very powerful and accurate imaging method of surfaces. As the measurement principle requires, geometric accurate micro-beams need to be used to relate the deflection of the beam to the applied tip force. The present paper proves that any type of not-straight beams could be used as the correlation between force and deflection could be found using analytical methods. A less familiar method to solve the differential equation that governs the relation between the two is proposed in the paper. This method is based on Lie group symmetry and it could be used to reduce the order of any differential equation that exhibits certain symmetry, by one order of magnitude. The sensitivity analysis of a non-straight micro-beam with large deflection subjected to point loads is carried out in the paper and the results of the analysis are presented. The case of multiple point loads is also presented as the literature gives analytical solution of large deflection of beams for a sole type of load. Lie group symmetry proves to be a powerful method that enables to analytically solve differential equations that cannot be solved by other methods.