Cart (Loading....) | Create Account
Close category search window
 

Nonlinear multimode dynamics and internal resonances of the scan process in noncontacting atomic force microscopy

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $31
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Hornstein, S. ; Department of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel ; Gottlieb, O.

Your organization might have access to this article on the publisher's site. To check, click on this link:http://dx.doi.org/+10.1063/1.4754814 

The focus of this paper is on the nonlinear multimode dynamics of a moving microbeam for noncontacting atomic force microscopy (AFM). An initial-boundary-value problem is consistently formulated, which includes both nonlinear dynamics of a microcantilever with a localized atomic interaction force, and a horizontal boundary condition for a constant scan speed and its control. The model considered is obtained using the extended Hamilton's principle, which yields two partial differential equations for the combined horizontal and vertical motions. The model incorporates, for the first time to our knowledge, two independent time-varying terms that depict the vertical base excitation of the AFM and the horizontal forcing term depicts the periodic scanning motion of the cantilever. Manipulation of these equations via a Lagrange multiplier enables construction of a modified equation of motion, which is reduced, via Galerkin's method, to a three-mode dynamical system, corresponding to finite amplitude AFM dynamics. The analysis includes a numerical study of the strongly nonlinear system culminating with a stability map describing an escape bifurcation threshold where the tip, at the free end of the microbeam, “jumps to contact” with the sample. Results include periodic, quasiperiodic, and non-stationary chaotic-like solutions corresponding to primary and secondary internal combination resonances, where the latter corresponds to energy balance between the cantilever modes.

Published in:

Journal of Applied Physics  (Volume:112 ,  Issue: 7 )

Date of Publication:

Oct 2012

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.