Abstract
This paper presents a new active controller technique effect of functionally graded (FG) cylindrical shell structure model within joint harmonic and parametric excitations. The new active controller involves Nonlinear Proportional-Derivative (NPD) plus Negative Cubic Velocity Feedback (NCVF) as a new nonlinear control method (NPDCVF). The motivation of this study is the well-known observation that NPDCVF control method can offer a means to improve the performance of plant systems. The coupled nonlinear differential equations with two modes have been derived applying the von Kármán nonlinear theory, Galerkin’s process, and the static condensation technique. Static condensation is the process of decreasing the number of free displacements or degrees of freedom. We have added other three different controller methods over the structure to select the best controller. The three applied controller methods to the considered structure are: Integral Resonant Control (IRC), Positive Position Feedback (PPF), and Nonlinear Integral Positive Position Feedback (NIPPF) which are applied to the considered structure. We establish that the best one for dipping the high vibration amplitudes is the NPDCVF as a new controller. The perturbation technique is useful to solve the present model including quadratic and cubic nonlinearities subjected to mixed harmonic and parametric forces within the simultaneous primary resonance case (Ω=ω1,Ω=ω2) as the worst resonance case of the system. All numerical outcomes have been completed with the help of MATLAB Ra 18.0 program software over the investigated model. The obtained results have proved that this new controller is excellent for improving the structure by reducing the risky vibrations caused during primary resonances. Frequency response equations have helped in observing the stability examination of the obtained numerical solutions. The actions of several factors performed on the controlled model have been examined and described. Some comparisons have also been prepared with the available recent published papers of a similar model.