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Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation

In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is base...

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Main Author: Cortés, Daniel (author)
Other Authors: Gutierrez, Alexander (author), Duque, Johan (author)
Format: article
Language:English
Published: 2022
Subjects:
Periodic solution
Cantilever vibrations
Atomic Force Microscope
Lower and upper solutions
Singularities
Ciencias Naturales y Exactas
Matemáticas
Matemática Aplicada
Online Access:https://hdl.handle.net/20.500.12381/3965
https://doi.org/10.1016/j.cnsns.2022.106396
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Summary:In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed.

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