Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy

被引：120

作者：

Ashhab, M ^{[1
]}

Salapaka, MV ^{[1
]}

Dahleh, M ^{[1
]}

Mezic, I ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Mech & Environm Engn, Santa Barbara, CA 93106 USA

来源：

NONLINEAR DYNAMICS | 1999年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

atomic force microscopy; chaotic behavior; Melnikov method; microcantilevers;

D O I：

10.1023/A:1008342408448

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

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.

引用

页码：197 / 220

页数：24

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