Microbeams with surface and piezoelectric effects in AFM

Abstract

Microbeam models with surface and piezoelectric effects are considered for atomic force microscopy (AFM). These models include rotatory inertia and shear deformation as proposed by Timoshenko and they are subject to forcing loads. Eigenanalysis of the free dynamic matrix model is performed with the use of a fundamental matrix response to determine the modal frequency equation and matrix mode shapes. The fundamental response governs the behaviour of a non-classical damped second-order matrix differential equation. It was observed that surface effects are influential for the natural frequency at the nanoscale. When the beam length increases from nanometers to microns, the surface effects disappear and the results converge into natural frequencies of classical Timoshenko model. Simulations with the piezoelectric model were performed to observe the effects of forcing pulses located at different positions of the microbeam.