Abstract
This paper presents a mixed active controller (NNPDCVF) that combines cubic velocity feedback with a negative nonlinear proportional derivative to reduce the nonlinear vibrating behavior of a nonlinear dynamic beam system. Multiple time-scales method treatment is produced to get the mathematical solution of the equations for the dynamical modeling with NNPDCVF controller. This research focuses on two resonance cases which are the primary and 1/2 subharmonic resonances. Time histories of the primary system and the controller are shown to demonstrate the reaction with and without control. The time-history response, as well as the impacts of the parameters on the system and controller, are simulated numerically using the MATLAB program. Routh-Hurwitz criterion is used to examine the stability of the system under primary resonance. A numerical simulation, using the MATLAB program software, is obtained to show the time-history response, the effect of the parameters on the system and the controller. An investigation is done into how different significant effective coefficients affect the resonance's steady-state response. The results demonstrate that the main resonance response is occasionally impacted by the new active feedback control's ability to effectively attenuate amplitude. Choosing an appropriate control Gaining quantity can enhance the effectiveness of vibration control by avoiding the primary resonance zone and unstable multi-solutions. Optimum control parameter values are calculated. Validation curves are provided to show how closely the perturbation and numerical solutions are related.