IRC controller for suppressing the vibrations of cantilever beam excited by an external force

Mahmoud, Sara Saad; Amer, Yeser; EL-Sayed, Ashraf; Abd EL_ Salam, M. N.

doi:10.21608/bfszu.2024.260691.1357

IRC controller for suppressing the vibrations of cantilever beam excited by an external force

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

² Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

³ Basic sciences department, Modern Academy

⁴ Basic sciences department, Higher Technological Institute, Tenth of Ramadan City

10.21608/bfszu.2024.260691.1357

Abstract

Vibration of structures is often an unwanted phenomena and should be avoided or controlled. In this paper, we study the effect of an integral resonant controller (IRC) on reducing the vibrations of the cantilever beam excited by an external force. The suggested system has two degree of freedom which is a non-linear system with the fifth and cubic nonlinearity terms excited by an external force. The second order approximate solutions of the system equation are sought using the multiple scale perturbation (MSPT). The frequency response equation is studied to test the behavior of the steady state solutions at the primary resonance case (Ω≅ω). The behavior of uncontrolled and controlled system is presented using time histories. Also, the stability of the system is investigated applying frequency response equation using the Runge-Kutta fourth order method. To scrutinize the time histories of the system before and after using IRC. The effects of different parameters of the system are studied numerically.

Keywords