Nonlinear modified positive position feedback control of cantilever beam system carrying an intermediate lumped mass

Abstract

In this paper, we investigated the nonlinear oscillations, stability and resonance of a cantilever beam system which carrying an intermediate lumped mass. The response of amplitudes and phases of the differential equation governing is derived applying the multiple scale perturbation (MSP) method. The nonlinear vibration control is analyzed using a new nonlinear modified positive position feedback (MPPF) approach. The nonlinear approximate solutions for this system up to and inclusive the second order approximation are solved. The influence of various parameters on the system response is studied. The numerical solutions and amplitude response of this system are also studied and investigated. The stability and bifurcation of the cantilever beam system is determined applying the frequency response curves and phase plane technique. Comparison between numerical and analytical solutions is illustrated. Results demonstrated that controller structure has the most salient role in the suppression performance. Utilizing the nonlinear MPPF approach, the vibration amplitude is suppressed at the exact resonant frequency sufficiently and the subsequent peaks of the frequency range is reduced significantly compared to the positive position feedback (PPF) approach.