Browsing by Author "Bek, M.A"

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    On the motion of a damped rigid body near resonances under the influence of harmonically external force and moments
    (Elsevier B.V., 8/31/2020) El-Sabaa, F.M; Amer, T.S.; Gad, H.M; Bek, M.A
    This paper presents the motion of a harmonically excited dynamical system with three degrees of freedom (3-DOF) in which it consists of a connected rigid body with a damped spring pendulum whose suspension point moves in a Lissajous curve path. Multiple scales method is utilized to obtain the asymptotic solutions of the equations of motion up to third approximation. Some types of resonances and the conditions of solvability for the steady state solutions have been clarified in light of the achieved modulation equations. The temporal representation of the achieved solutions and resonance curves are presented in some plots to show the good effect of the distinct parameters on the dynamical motion of the investigated system. The numerical solutions of the governing system of motion are gained utilizing the Runge–Kutta method from fourth order. The comparison between these solutions and the analytical ones reflects the good accuracy of the analytical solutions and the used perturbation techniques
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    The vibrational motion of a spring pendulum in a fluid flow
    (Elsevier B.V., 2020-12) Bek, M.A; Amer, T.S; Sirwah, M.A; Awrejcewicz, J; Arab, A.A
    In this work, the response of two degrees of freedom for a nonlinear dynamical model represented by the motion of a damped spring pendulum in an inviscid fluid flow is investigated. The governing system of motion is obtained using Lagrange’s equations. The equations of this system are solved utilizing the multiple scales method to obtain the asymptotic solutions up to the second approximation. Resonance cases of the system are classified and the modulation equations are achieved. The steady state solutions are examined in view of the solvability conditions. The dynamical behavior regarding the time history of the considered motion, the resonance curves and the steady state solutions are performed graphically. The effect of different parameters on the motion is analyzed using non-linear stability analysis. The importance of this model is due to its various applications which centric on engineering vibrating systems.