摘要
相比于整数阶微谐振器,分数阶微谐振器能更准确模拟微谐振器系统。利用分数阶微分及其理论,提出分数阶微谐振器系统模型,并通过预估-校正法对系统动力学方程进行数值分析。在分数阶微谐振器中,存在两项分数阶次,p 1为反映系统材料粘弹性特性的微分项阶次,p 2为反映系统内部热阻尼的阻尼项阶次。研究表明:p 1的变化是导致系统混沌现象产生的主要因素;随着p 1的变化,系统以倍周期分岔和阵发性突变的方式进入到混沌运动状态。
Compared to integer-order microresonators,fractional-order microresonators can more accurately simulate micro-resonator systems.Based on the fractional-order differential and its theory,a fractional-order microresonator system model was proposed,and the system dynamics equation was numerically analyzed by the predictor-correction method.In the fractional-order microresonator,there are two fractional orders,p 1 is the differential term order reflecting the viscoelastic properties of the system material,and p 2 is the damping term order reflecting the internal thermal damping of the system.The research shows that the change of p 1 is the main factor leading to the chaotic phenomenon of the system.With the change of p 1,the system enters the chaotic motion state by means of double-cycle bifurcation and paroxysmal mutation.
作者
席涛
谢进
孙建华
魏巍
XI Tao;XIE Jin;SUN Jian-hua;WEI Wei(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China)
出处
《仪表技术与传感器》
CSCD
北大核心
2019年第11期87-90,94,共5页
Instrument Technique and Sensor
基金
国家自然科学基金项目(51575457)
关键词
分数阶
微谐振器
材料粘弹性
热阻尼
混沌运动
fractional order
microresonator
material viscoelastic
thermal damping
chaotic motion
