Subharmonic Solutions of Governed MEMS System Subjected to Parametric and External Excitations
A. M. El-Naggar, K. M. Khalil, A. M. Omran
Asian Research Journal of Mathematics · pp. 1–13 · Published 8 Aug 2017
10.9734/ARJOM/2017/32008Abstract
Subharmonic periodic solutions of order (1/2 ,1/4) to a weakly second order ordinary differential equation which governed the motion of a micro-dynamical system are studied analytically. Applying the method of multiple scales, we derive the modulation equation in the amplitude and the phase of each type of periodic solutions. Determine the steady-state solutions (fixed-points of the modulation equation). Obtained the frequency-response equation (The relation between the amplitude and the detuning parameter and other parameter in the differential equation). Stability analysis of the steady-state solutions is given. Numerical study of the frequency-response equation are carried out. The results are presented in a group of Figures in which solid (dashed) curves indicated stable (unstable) preiodic solutions.
Cited by 0
No indexed citations yet.
Related research
- Superharmonic Solutions of Order (2,3) to a MEMS Governed the Motion of a TM-AFM Cantilever — shares topic coverage
- Harmonic and Sub-Harmonic Periodic Solutions (1/2, 1/3) of Generalized Mathieu-Van der Pol-Duffing Equations — shares topic coverage
- Suppression of Vibrations of a Forced and Self-excited Nonlinear Beam by Using Positive Position Feedback Controller PPF — shares topic coverage
- Periodic Solutions of a Modified Duffing Equation Subjected to a Bi-Harmonic Parametric and External Excitations — shares topic coverage
- Self-similar Solutions for a Nonlinear Heat Equation Modelling MEMS — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
0
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.