Mehran Ghomshibozorg (PhD)
Year: 2005 - 2014
Thesis Title: Dynamic Stability Analysis of Flexible Beam Vibration subjected to Consecutive Moving of a Mass
Thesis Abstract: In this research, a time-domain analysis of an Euler-Bernoulli beam subjected to the periodic passage of vehicles is investigated. The beam-moving mass interaction causes dynamic stability issue in the beam vibration which is studied using Floquet theory, Homotopy perturbation method (HPM) and Homotopy analysis method (HAM) that permit to present the results in the form of stability maps.
The effect of the modelling method for the beam-traversing object interaction system has been quantitatively and qualitatively studied by Floquet theory. Three models considered for the moving vehicle include a point mass, a mass with suspension system and a rigid body with suspension system. The results are presented as stability maps in mass-velocity diagrams. The results indicate that the modelling method has significant influence on the dynamic stability analysis and dynamic response of the system. Results also show increase of the suspension system characteristics (mass ratio, natural frequency and damping ratio) and decrease of length of rigid body affect the stability margin in the mass-speed diagram and extend the unstable zone. Another conclusion indicates that ignoring nonlinear terms in the moving mass acceleration could lead to an incorrect analysis of the system stability. Any variation in the physical and geometric properties of the beam that leads to a decrease of its natural frequency or any reduction of the repetitive traversing period or increase of the compressive axial load will extend the unstable zone. Although beam damping coefficient doesn’t have significant effect on the stability border, nonetheless any increment of this coefficient lessens the instability rate.
Using Homotopy analysis and Homotopy perturbation methods, a semi-analytical results has been determined for the stable/unstable boarder line. It has been completely matched the numerical results obtained by Floquet theory analysis. In addition the HAM and HPM analyses resulted in a new sets of curves where locates the resonant points in the stable region.
In addition to the stability analysis, vibration control of the beam-moving mass system has been performed using LQR, fuzzy control and adaptive fuzzy control methods with the control input force exerted at the middle of the beam. The numerical simulations show that LQR and fuzzy control methods can control vibrations in the critical conditions in the system with no uncertainty. For the case of an uncertain system, a direct model reference adaptive fuzzy controller is proposed to control the system. It has been concluded from numerical simulation results that the controller is fully capable to control the vibration of the beam in cases like irregular passage of the moving objects with the different masses and velocities.
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