Vibration Study of Rotating Rigid Hub and a Flexible Composite Beam under Simultaneous Primary-internal Resonance
M. Kamel *
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menouf, Menoufia University, Egypt.
H. El-Gohary
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menouf, Menoufia University, Egypt.
H. M. Shawky
Department of Mathematics, Faculty of Science, Al-Azhar University, (Girl’s Branch), Egypt.
H. Mosaa
Department of Mathematics, Faculty of Science, Al-Azhar University, (Girl’s Branch), Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the vibration of a composite system consisting of a rotating rigid hub and a flexible thin-walled beam is considered and studied. The equation of motion is derived in the previous work of Warminski and Latalski. The method of multiple scale technique has been applied to obtain frequency response equations near the simultaneous internal and primary resonance case in the absence of the acceleration of the hub. The vibration stability at this resonance case is investigated from the frequency response equations and studied using Liapunov’s methods. The effects of changes in selected structural parameters on the vibrating system behavior are investigated and studied numerically. Through the performed studies of the effects of changes in selected system a shift of the steady state amplitudes and the multi-valued of the bent curves are observed and the steady state amplitudes of the beam and hub have decreasing in the instability regions for natural frequencies. Finally, a comparison with the papers of previously published work is reported.
Keywords: Simultaneous primary resonance, frequency response curves, system stability, jump phenomenon