Mixed controller (IRC+NSC) involved in the harmonic vibration response cantilever beam model

Abstract

This manuscript aims for improving the vibrational behaviors of a cantilever beam model through an intermediate lumped mass via offering a new control methodology to suppress for such high oscillations of the system. The equation of the considered cantilever beam structure is gained applying Euler–Lagrange technique. Accordingly, the considered model is modified by mixing Integral Resonant Control (IRC) along with the Nonlinear Saturation Controller (NSC) as anew controller to the considered system. Due to the recommended control technique, the modified system model is studied and analyzed by the perturbation technique. Time histories figures of the measured system plus the new controller are involved to display the response before and after control. The frequency response figures of the modified model before and after new controller near simultaneous condition ( Ω ≈ ω 1 , ω 1 ≈ 2 ω 2 ) are gained. Each frequency-response curves have stable and unstable regions are determined numerically. Numerical results show the vibrations of the system are eliminated when adding combined IRC and NSC controllers. Finally, numerical outcomes are performed that illustrated an excellent agreement with the analytical ones. Comparison between this paper and recent papers of the cantilever beam are done.