基于分数阶阻尼的超磁致伸缩致动器非线性动力学研究  

Nonlinear Dynamics Study of Giant Magnetostrictive Actuator Systems Based on Fractional Damping

作　　者：闫洪波[1] 付鑫 汪建新[1] 于均成 YAN Hongbo;FU Xin;WANG Jianxin;YU Juncheng(College of Mechanical Engineering,Inner Mongolia University of Science&Technology,Baotou 014010)

机构地区：[1]内蒙古科技大学机械工程学院,包头014010

出　　处：《机械工程学报》2022年第23期151-163,共13页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51365033);内蒙古自然科学基金(2020LH05023)资助项目。

摘　　要：为进一步揭示超磁致伸缩致动器(Giant magnetostrictive actuator,GMA)系统非线性运动过程中的内在机理和动力学特征,基于分数阶微积分理论,将GMA动力学系统模型拓展至分数阶,建立含有分数阶阻尼的非线性GMA系统动力学方程,基于平均法分析系统主共振,得到系统的幅频响应方程;使用幂级数方法求解系统的数值解,通过Matlab数值模拟分析不同激励幅值和阻尼阶次对GMA系统的影响机理,从定性和定量的角度研究系统的分岔和混沌运动现象。结果表明:激励幅值和阻尼阶次对系统的幅频特性有显著影响;阻尼阶次对系统的分岔和混沌行为影响较大;不同阻尼阶次下由激励幅值变化引起系统的动力学行为相似但混沌区域不同。该研究有助于更好地了解GMA系统动力学特性,对工程实践中控制GMA系统稳定运行提供新的视角。To better further reveal the inherent mechanism and dynamic characteristics of the nonlinear motion of the giant magnetostrictive actuator(GMA) system, based on the fractional calculus theory, a GMA dynamic system model is extended to the fractional order, and a model containing fractional damping is established. The nonlinear GMA dynamic system equation is based on the average method to analyze the main resonance of the system, and the amplitude-frequency response equation of the system is obtained;the numerical solution of the system is solved by the power series method, and the different excitation amplitudes and damping orders are analyzed by Matlab numerical simulation. Influence mechanism on GMA system, study the bifurcation and chaotic motion phenomenon of the system from the qualitative and quantitative point of view. The results show that the excitation amplitude and damping order have a significant impact on the amplitude-frequency characteristics of the system;the damping order has a great influence on the bifurcation and chaotic behavior of the system;the dynamics of the system are caused by the change of the excitation amplitude under different damping orders The behavior is similar but the chaos area is different. This research is helpful to better understand the dynamic characteristics of the GMA system and provides a new perspective for controlling the stable operation of the GMA system in engineering practice.

关 键 词：超磁致伸缩致动器 分数阶微积分 分岔 混沌特性 定性和定量分析 

分 类 号：O332[理学—一般力学与力学基础]