Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy

M. Ashhab, M. V. Salapaka, M. Dahleh, I. Mezić

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126 Scopus citations


We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard-Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction.

Original languageEnglish (US)
Pages (from-to)197-220
Number of pages24
JournalNonlinear Dynamics
Issue number3
StatePublished - 1999

Bibliographical note

Funding Information:
This research was supported by the National Science Foundation under Grants 9632820, ECS-9733802, and AFOSR under Grant No. F49620-97-1-0168.


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