Staff Members - Benha University
Harmonic Solution of a Weakly Non-linear Second Order Diff erential Equation Governed the Motion of a TM-AFM Cantilever
British Journal of Mathematics & Computer Science • 2016
Publication Information
Authors
A M Elnaggar; K M Khalil; A S Rahby
Keywords
Micro-electro-mechanical system (MEMS); atomic force microscopy (AFM); di erential
equation; harmonic solution; multiple scales method.
Journal
British Journal of Mathematics & Computer Science
Publisher
Not Available
Volume
15
Issue
4
Pages
1-11
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
The harmonic solution of a weakly non-linear second order differential equation governed the
dynamic behavior of a micro cantilever based on TM (Tapping mode) AFM (Atomic force
microscope) is investigated analytically by applying the method of multiple scales (MMS).
The modulation equations of the amplitude and the phase are obtained, steady state solutions,
frequency response equation, the peak amplitude with its location and the approximate analytical
expression are determined. The stability of the steady state solutions is calculated. Numerical
solutions of the frequency response equation and its stability condition are carried out for
different values of the parameters in the equation. Results are presented in a group of figures.
Finally discussion and conclusion are given
dynamic behavior of a micro cantilever based on TM (Tapping mode) AFM (Atomic force
microscope) is investigated analytically by applying the method of multiple scales (MMS).
The modulation equations of the amplitude and the phase are obtained, steady state solutions,
frequency response equation, the peak amplitude with its location and the approximate analytical
expression are determined. The stability of the steady state solutions is calculated. Numerical
solutions of the frequency response equation and its stability condition are carried out for
different values of the parameters in the equation. Results are presented in a group of figures.
Finally discussion and conclusion are given