Nonlinear vibration of AFM microcantilevers with sidewall probe

In this paper, an atomic force microscope (AFM) with an assembled cantilever probe (ACP) capable of measurement at sidewalls and edges is modeled and its nonlinear vibration is investigated. The ACP comprises a horizontal microcantilever, a vertical assembled extension located at the free end of the...

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Bibliographic Details
Published inJournal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 39; no. 12; pp. 4873 - 4886
Main Author Vatankhah, R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects
Amplitude modulation
Atomic force microscopes
Atomic force microscopy
Engineering
Frequency modulation
Galerkin method
Hamilton's principle
Mechanical Engineering
Microscopes
Nonlinearity
Ordinary differential equations
Partial differential equations
Perturbation methods
Technical Paper
Vibration measurement
Atomic force microscopy (AFM)
Nonlinear vibration
Perturbation techniques
Micro-structures
Nonlinear dynamics analysis
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Summary:In this paper, an atomic force microscope (AFM) with an assembled cantilever probe (ACP) capable of measurement at sidewalls and edges is modeled and its nonlinear vibration is investigated. The ACP comprises a horizontal microcantilever, a vertical assembled extension located at the free end of the microcantilever and a tip located at the free end of the extension. Utilizing Hamilton principle, the governing partial differential equation (PDE) of the ACP vibration and corresponding boundary conditions are obtained. Subsequently, the governing ordinary differential equation (ODE) is derived applying Galerkin method to the aforementioned PDE. Since the ODE is nonlinear, perturbation techniques are employed to solve it for two major functional modes of AFMs: amplitude modulation (AM) and frequency modulation (FM). Effects of different factors including geometrical parameters on the frequency responses of the system are delineated during some figures in which the jump phenomena can be observed. The results show that the system becomes more nonlinear as the length of the vertical extension increases; however, increase of the tip length has a decreasing effect on the nonlinearity of the system.
ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-017-0823-8