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2 Journal of Applied Mathematics and Computational Mechanics

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Optimal passive structural control under extreme earthquake excitations using a combined pendulum tuned mass damper

Kamel Abanoub G., Basily Remon M.

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 4

51--64

Many engineering applications utilize passive Tuned Mass Dampers (TMDs) in several engineering applications because of their simplicity, readiness, and their ability in attenuating structural vibrations exposed to mild or extreme earthquake excitations. The main aim of this work is to find the optimum values of the system parameters after attaching a three degree of freedom Combined Pendulum Tuned Mass Damper (3-DOF CPTMD) to the main structure to investigate if the proposed solution will assist in reducing the amplitudę of the vibration. Three optimization search techniques are utilized, and the best optimum method is determined. Moreover, the structural system was modelled mathematically to get the governing motion equations, and the system was put into state-space format before being simulated using a homemade MATLAB© code. Additionally, it is found that the proposed 3-DOF CPTMD is very effective in dampening the structural vibrations under various earthquake excitations (including extreme conditions)

Numerical simulation of channel flow over a skewed equilateral cavity

Kamel Abanoub G., Haraz Eman H., Hanna Sarwat N.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

29--43

In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions’ method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.