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. Te modeling equations with piezoelectric and surface scale efects are written as a matrix diferential 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 efects. Simulations were performed for a two stepped beam with a piezoelectric patch subject to pulse forcing terms. Results with Timoshenko models that include surface efects are presented for micro- and nanoscale. It was observed that the efects are signifcant just in nanoscale. We also simulate the frequency efects of a doublespan beam in which one segment includes rotatory inertia and shear deformation and the other one neglects both phenomena. Te proposed analytical methodology can be useful in the design of micro- and nanoresonator structures that involve deformable fexural models for detecting and imaging of physical and biochemical quantities.