Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects

Abstract

Vibration dynamics of elastic beams that are used in nanotechnology, such as atomic force microscope modeling and carbon nanotubes, are considered in terms of a fundamental response within a matrix framework. The modeling equations with piezoelectric and surface scale effects are written as a matrix differential equation subject to tip-sample general boundary conditions and to compatibility conditions for the case of multispan beams. We considered a quadratic and a cubic eigenvalue problem related to the inclusion of smart materials and surface effects. Simulations were performed for a two stepped beam with a piezoelectric patch subject to pulse forcing terms. Results with Timoshenko models that include surface effects are presented for micro- and nanoscale. It was observed that the effects are significant just in nanoscale. We also simulate the frequency effects of a double-span beam in which one segment includes rotatory inertia and shear deformation and the other one neglects both phenomena. The proposed analytical methodology can be useful in the design of micro- and nanoresonator structures that involve deformable flexural models for detecting and imaging of physical and biochemical quantities.