分数阶阻尼GMA系统主共振振动特性研究  

Study on primary resonance vibration characteristics of fractional damped GMA system

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

机构地区：[1]内蒙古科技大学机械工程学院,内蒙古包头014010

出　　处：《传感器与微系统》2023年第5期65-68,共4页Transducer and Microsystem Technologies

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

摘　　要：为更精确表达超磁致伸缩致动器(GMA)的动力学特性,研究了含分数阶阻尼的GMA磁滞非线性系统的受迫振动。利用分数阶微积分描述GMA磁滞非线性系统的阻尼力,建立具有分数阶阻尼的GMA动力学方程;利用平均法得到GMA系统的近似解析解,对含有分数阶阻尼的GMA系统进行主共振分析,得到系统稳定时的条件和幅频响应方程。使用MATLAB软件分析分数阶阻尼力对系统动力学的影响,对系统主共振幅频响应的解析解与数值解进行比较,发现两者符合程度较高;详细分析分数阶阻尼对GMA磁滞非线性系统主共振幅频响应的影响,相比于整数阶系统得到更为丰富的非线性现象,对控制和预测系统的输出响应具有重要意义。In order to express dynamic characteristics of giant magnetostrictive actuator(GMA)more accurately,the forced vibration of GMA hysteresis nonlinear system with fractional damping is studied.The damping force of GMA hysteresis nonlinear system is described with fractional differential,and the GMA dynamic equation with fractional damping is established.The approximate analytical solution of the GMA system is obtained using the averaging method.The principal resonance analysis of the GMA system with fractional damping is carried out,and the stability conditions and amplitude-frequency response equations of the system are obtained.The influence of fractional damping force on system dynamics is analyzed with MATLAB software,and the analytical solution of the primary resonance amplitude frequency response of the GMA system is compared with the numerical solution,and it is found that the two solutions are in good agreement with each other.The influence of fractional damping on the primary resonance amplitude frequency response of GMA hysteresis nonlinear system is analyzed in detail,more abundant nonlinear phenomena is obtained than integer order system,which is of great significance to control and predict the output response of the system.

关 键 词：分数阶微分 超磁致伸缩致动器 动力学方程 主共振 平均法 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置] O332[自动化与计算机技术—控制科学与工程]