Suppression of Vibrations of a Forced and Self-excited Nonlinear Beam by Using Positive Position Feedback Controller PPF

Al-Azhar Bulletin of Science

EL-Sayed

Saleh

et al. 2019

In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the behavior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum working conditions for the PPF controller. The stability analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented.

Section: Introductionmentioning

confidence: 99%

Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Al-Azhar Bulletin of Science

EL-Sayed

Saleh

et al. 2019

“…A quantitative investigation of the nonlinear behavior of a forced and self-excited beam with a positive position feedback controller PPF was reported. So that the external excitation is a harmonic motion on the cantilever beam's support [19].…”

Section: Introductionmentioning

confidence: 99%

Mix active control feedback of a continuously rotating shaft's nonlinear oscillations through simultaneous resonance

EL-Sayed

Elsayed

2023

Preprint

In our consideration, mix active controller negative velocity and acceleration feedback are presented to eliminate the vibration of the nonlinear oscillations of a continuous rotating shaft at one of the worst simultaneous resonance cases Ω=ω1,ω2=ω1 . The system presented by two degree of freedom containing the third order of nonlinear terms and multi external forces. The multiple scale method used to obtain the approximate solution of the vibrating system. The frequency response equation is used to investigated the stability of controlled system. We examined at the system numerically to compare the time histories before and after adding a negative velocity and acceleration feedback controller. We analyzed the performance of several selected parameters of the studied system for response curves. Finally, the numerical solution and the approximate solution obtained from the multiple scale are in good agreement.

“…If the stability conditions are not satisfied, the amplitude of the Van der Pol oscillator increases, according to [5][6][7]applying the method of multiple time scale MTSPT of hybrid Van der Pol-Duffing-Rayleigh oscillator for modelling the lateral walking force on a rigid floor and Investigations on the bifurcation of a noisy, quantitative analysis of the nonlinear behavior of the forced and self-excited beam was studied. [8]. modulated and displayed the Van der Pol -Duffing -Rayleigh oscillator bifurcation analysis.…”

Section: Introductionmentioning

confidence: 99%

The behavior of the vibration for nonlinear system with max active controller.

Elsayed

Bulletin of Faculty of Science, Zagazig University

2023

Vibration control can be divided into two main categories : passive control and active control. Active control is provided by the negative linear velocity and acceleration feedback controller. The vibration of a nonlinear dynamical system is reduced by the Negative linear velocity and acceleration feedback controller in the worst resonance case (   ).This system has one degree of freedom, which contains the third order of nonlinear terms, as well as an external force. The response of the nonlinear system is determined using the multiple scale perturbation technique. Frequency response equations are used to test the stability of the numerical solution. The impacts of different parameters on the vibrating system is studied and reported on. Numerically, we investigated the time histories of the system before and after using Negative linear velocity acceleration feedback controller using Runge -Kutta of the fourth order and studied the response curve with detuning parameter  . Finally, the approximate and numerical solutions accord well.