摘要
研究了谐波激励下分数阶平方阻尼Mathieu振子的主共振。首先采用多尺度法得到了主共振的近似解析解,利用数值方法验证了近似解的准确性。然后建立了系统定常解的幅频曲线方程,基于Lyapunov第一方法得到了稳态响应的稳定性条件,分析了强迫主共振和参激共振下系统特有的幅频特性。最后通过数值仿真研究了分数阶微分项对系统幅频特性的影响。结果表明,利用分数阶微分项系数和阶次能对系统响应幅值和振动频率等形成一种双重调节,可有效改善系统幅频特性。
In this research,the primary resonance of quadratic damping Mathieu oscillator with fractional-order derivative under forced excitation was studied.Firstly,the method of multiple scales was used to seek the approximate analytical solution of the primary resonance and its accuracy was verified by numerical method.Moreover,the amplitude-frequency response equation was established,first method based on Lyapunov was used to quantitatively calculate the stability condition of the steady-state response,and the amplitude-frequency responses of the system were analyzed.Finally,the effects of fractional differential term on the amplitude-frequency curves of the system were investigated by numerical simulation.It is found that the fractional differential term has dual regulation functions on the response amplitude and vibration frequency of the system,which is applicable to optimize the system.
作者
郭建斌
申永军
Guo Jianbin;Shen Yongjun(School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)
出处
《石家庄铁道大学学报（自然科学版）》
2022年第3期98-103,共6页
Journal of Shijiazhuang Tiedao University(Natural Science Edition)
基金
国家自然科学基金(U1934201)
石家庄铁道大学研究生创新项目(YC2021043)。
关键词
Mathieu振子
分数阶微分
主共振
稳定性
Mathieu oscillator
fractional-order derivative
primary resonance
stability
