The improved giant magnetostrictive actuator oscillations via positive position feedback damper

Hany Bauomy; A. T. EL-Sayed; A. M. Salem; F. T. El-Bahrawy; Hany Bauomy; A. T. EL-Sayed; A. M. Salem; F. T. El-Bahrawy

doi:10.3934/math.2023862

AIMS Mathematics

2023, Volume 8, Issue 7: 16864-16886. doi: 10.3934/math.2023862

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The improved giant magnetostrictive actuator oscillations via positive position feedback damper

1.
Department of Mathematics, College of Arts and Science in Wadi Addawasir, Prince Sattam Bin Abdulaziz University, P.O. Box 54, Wadi Addawasir 11991, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Department of Basic Science, Modern Academy for Engineering and Technology, El-Hadaba ElWosta, Elmokattam 11439, Egypt

Received: 17 February 2023 Revised: 23 April 2023 Accepted: 24 April 2023 Published: 15 May 2023
MSC : 34A34, 37N35, 70J99, 70K20, 74H10

This article contemplates the demeanor of the giant magnetostrictive actuator (GMA) when a positive position feedback (PPF) damper is used to enable tight control over its vibration. The methodology followed here mathematically searches for the approximate solution for the motion equations of the GMA with the PPF damper, which has been accomplished by using one of the most famous perturbation methods. The multiple scale perturbation technique (MSPT) of the second-order approximation is our strategy to obtain the analytical results. The stability of the system has also been investigated and observed by implementing frequency response equations to close the concurrent primary and internal resonance cases. By utilizing Matlab and Maple programs, all numerical discussions have been accomplished and explained. The resulting influence on the amplitude due to changes in the parameters' values has been studied by the frequency response curves. Finally, a comparison between both the analytical and numerical solutions using time history and response curves is made. In addition to the comparison between our PPF damper's effect on the GMA, previous works are presented. To get our target in this article, we have mentioned some important applications utilized in the GMA system just to imagine the importance of controlling the GMA vibration.
- vibration control,
- GMA,
- frequency response equation,
- stability,
- PPF control,
- multiple scale perturbations
Citation: Hany Bauomy, A. T. EL-Sayed, A. M. Salem, F. T. El-Bahrawy. The improved giant magnetostrictive actuator oscillations via positive position feedback damper[J]. AIMS Mathematics, 2023, 8(7): 16864-16886. doi: 10.3934/math.2023862

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Abstract

This article contemplates the demeanor of the giant magnetostrictive actuator (GMA) when a positive position feedback (PPF) damper is used to enable tight control over its vibration. The methodology followed here mathematically searches for the approximate solution for the motion equations of the GMA with the PPF damper, which has been accomplished by using one of the most famous perturbation methods. The multiple scale perturbation technique (MSPT) of the second-order approximation is our strategy to obtain the analytical results. The stability of the system has also been investigated and observed by implementing frequency response equations to close the concurrent primary and internal resonance cases. By utilizing Matlab and Maple programs, all numerical discussions have been accomplished and explained. The resulting influence on the amplitude due to changes in the parameters' values has been studied by the frequency response curves. Finally, a comparison between both the analytical and numerical solutions using time history and response curves is made. In addition to the comparison between our PPF damper's effect on the GMA, previous works are presented. To get our target in this article, we have mentioned some important applications utilized in the GMA system just to imagine the importance of controlling the GMA vibration.

References

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