IJPAM: Volume 28, No. 1 (2006)

1:4 INTERNAL RESONANCE ACTIVE ABSORBER FOR
NON-LINEAR VIBRATING SYSTEM

S. El-Serafi$^1$, M. Eissa$^2$, T.H. El-Ghareeb$^3$
$^{1,2}$Department of Engineering Mathematics
Faculty of Electronic Engineering
Menouf, 32952, EGYPT
$^{3}$Department of Mathematics
Faculty of Education
Suez Canal University
Suez, EGYPT
e-mail: taha_elghareeb@yahoo.com


Abstract.In this paper we present a mathematical study of active control in some non-linear differential equations, representing a single degree of freedom system like an aircraft wing subjected to multi-excitation forces is considered and solved using the method of multiple scale perturbation. The system is considered with 1:4 internal resonance active control absorber. The approximate solutions are derived up to the second order approximation. The stability of the system is investigated applying both frequency response equations and phase plane methods. The main system vibration can be reduced at the resonance worst case via active control. Some recommendations are given at the end of the work.

Received: April 11, 2006

AMS Subject Classification: 34A34

Key Words and Phrases: control, active, absorber, absorber effectiveness

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 1