Browsing by Author "Hamed, Y. S."
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- Absolutely stable difference scheme for a general class of singular perturbation problemsPublication . El-Zahar, Essam R.; Alotaibi, A. M.; Ebaid, Abdelhalim; Baleanu, Dumitru; Machado, J. A. Tenreiro; Hamed, Y. S.This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.
- Utilizing Macro Fiber Composite to Control Rotating Blade VibrationsPublication . Hamed, Y. S.; Kandil, Ali; Machado, José TenreiroThis work applies an active control algorithm, using a macro fiber composite (MFC) to mitigate the unwanted vibrations of a rotating blade. The algorithm is a second-order oscillator, having the positive displacement signal of the blade for input and the suitable control force to actuate the blade for output. This oscillator is linearly coupled with the blade, having in mind that their natural frequencies must be in the vicinity of each other. The rotating blade is modeled by representing two vibrational directions that are linearly coupled. An asymptotic analysis is considered to understand the resulting nonlinear phenomena. Several responses are included to portray the dynamical behavior of the system under control. From the results, we observe the asymmetry between the blade’s vibrational directions. Moreover, a verification is included for comparing the analytical and numerical results.