Department of Mathematics, College of Arts and Science in Wadi Addawasir, Prince Sattam Bin Abdulaziz University, P.O. Box 54, Wadi Addawasir 11991, Saudi Arabia.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt.
Math Biosci Eng. 2023 Jan 9;20(3):5135-5158. doi: 10.3934/mbe.2023238.
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.
本文提出了一种混合主动控制器（NNPDCVF），将立方速度反馈与负非线性比例导数相结合，以减少非线性动力梁系统的非线性振动行为。采用多时间尺度方法处理，得到了具有 NNPDCVF 控制器的动力建模方程的数学解。本研究集中于两个共振情况，即主共振和 1/2 次谐共振。显示了没有控制和有控制时主系统和控制器的时间历史，以证明它们的反应。使用 MATLAB 程序对时间历史响应以及系统和控制器参数对系统的影响进行了数值模拟。劳斯-胡尔维茨准则用于检查主共振下系统的稳定性。使用 MATLAB 程序软件进行数值模拟，以显示时间历史响应、系统和控制器参数的影响。研究了不同显著有效系数如何影响共振的稳态响应。结果表明，主共振响应偶尔会受到新的主动反馈控制有效衰减幅度的能力的影响。选择适当的控制增益可以通过避免主共振区和不稳定的多解来提高振动控制的有效性。计算了最优控制参数值。提供了验证曲线，以显示摄动和数值解之间的关系有多密切。
