טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMaimon Ronen
SubjectNonlinear Vibrations of Micro-Beams in Atomic
Force Microscopy
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Oded Gottlieb
Professor Alon Hoffman


Abstract

Micro-beams in non-contact atomic force microscopy are extremely sensitive sensors that map sample surfaces down to atomic resolution. The sensitivity of system dynamics to slight boundary changes also enables estimation of the atomic interaction forces. These microbeams are forced at the clamped edge and interact with the surface at the free edge. This interaction yields a complex nonlinear dynamical system which requires comprehensive modeling and analysis.

            This thesis includes a dynamical system model as an Euler- Bernoulli beam subject to a nonlinear boundary condition for the atomic interaction at the free edge. Solution of the nonlinear system using an asymptotic multiple-scales method is developed near primary and secondary resonances. Furthermore, a set of controlled experiments with different material samples and various conditions, were conducted to validate the theoretical prediction. The materials surfaces included silicon, diamond and graphite.

            The results of the asymptotic analysis yield the system frequency response. Near primary resonance, a unique solution was obtained where the maximum amplitude is smaller than the linear response. Multiple coexisting solutions were also determined for low damping. System response near secondary resonances includes a supper-harmonic frequency response and conditions for existence of sub-harmonic resonance.

            The experimental results include a measured nonlinear frequency response that depends on the interaction distance for different samples. These results enable estimation of dynamic system parameters for each material tested. The combination of theoretical nonlinear analysis and experiments enable characterization of graphite grown on a diamond sample.

            A nonlinear dynamical model was developed and analyzed for the response of a microbeam in noncontact atomic force microscopy. Comparison of theoretical results with experiments will enable examination of candidate atomic interaction potentials, and identification of nonlinear interaction parameters in hybrid materials.