Dynamic modeling and nonlinear vibration simulation of piezoelectric micro-beam in self sensing mode of atomic force microscope

Nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. In this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  This paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triangular head, in self-measure mode and close proximity to the surface of a sample. Output charge from the piezoelectric layer and also the output current, in this mode, is considered as an effective factor in the measurement of the bending. The micro cantilever’s vibration behavior becomes nonlinear, as it approaches the surface of the sample. Surely the piezoelectric layer in the self-measure mode can be considered as a good measuring tool, only when it reflects the effects of the nonlinear interaction between the tip of the probe and the surface of the sample in its measurements. In order to investigate this matter, first the differential equations that are ruling over the vibrating movements of the piezoelectric micro cantilever with a triangular head, are transformed into normal nonlinear differential equations using the Galerkin method. Then the resulting nonlinear differential equation is solved using the multi-scale method. After solving the differential equation ruling over the problem, the micro cantilevers behavior in the proximity of the surface of the sample is simulated and the effect of factors such as balancing distance, oscillation modes and the substance of piezoelectric layer are investigated.