טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentFainshtein Emanuel
SubjectNonlinear Dynamics and Stability of Piezoelectric Microbeams
with Application for Atomic Force Microscopy
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oded Gottlieb


Abstract

The focus of this research is on the nonlinear dynamics and stability of piezoelectric microbeams, which are commonly used for Atomic Force Microscopy (AFM). The AFM is used for imaging and mapping surfaces down to the atomic level. The mapping includes a scan process where a micro - cantilever, which has a tip mounted at its free end, is modulated in close proximity to the surface. In the past decade, the need for increased scan speed led to design of an AFM microbeam array. Control of such a system is achieved by making use of individually actuated piezoelectric beam elements, as the map cannot be done with base excitation of the complete array. The accuracy of force estimation from measured data depends crucially on the quality of the mathematical model used predict system response. A typically used model is that of a lumped mass system that reduces the beam to a linear spring with a nonlinear restoring force derived from an interaction between the tip and the sample. This model does not incorporate the dynamic piezoelectric exciting moment or the possible material nonlinearities introduced by the conducting piezoelectric layer. Thus, the research objective is to develop and analyze a continuum model for the AFM that consistently incorporates both nonlinear atomic interaction with the geometric and material nonlinearities of the piezoelectric microbeam. The analysis employs an asymptotic multiple scale method, which enables investigation of weakly nonlinear solutions near primary, secondary and internal resonances. Results include experimental validation of the theoretical system response for a symmetric macrobeam configuration and numerical verification of the asymmetric AFM dynamical system.