摘要
用平均法研究了含分数阶导数项的van der Pol-Duffing振子的动力学行为和力传递率。得到了主共振时振子的一阶解析解、定常解幅频曲线和相频曲线的解析表达式,进一步通过与数值解作对比,验证了解析解的正确性,分析了不同参数对幅频曲线和力传递率的影响。结果表明:解析解与数值解吻合良好;在无量纲情况下,共振区分数阶项系数、非线性参数、分数阶阶次、阻尼比对幅频曲线和力传递率的共振峰值均有抑制作用;不同频率区段参数对隔振效果的影响不同,在低频隔振区非线性参数和幅值越小隔振效果越好,此外阻尼比对力传递率影响很小;在高频隔振区增大非线性参数、幅值和阻尼比有助于提高隔振效果。
Here,dynamic behavior and force transmissibility of van der Pol-Duffing oscillator with fractional-order derivative term were studied with the average method.Firstly,analytical expressions during main resonance of the oscillator’s the first-order analytical solution,steady solution’s amplitude-frequency curve and phase-frequency curve were obtained.Then,the correctness of the analytical solution was verified by comparing it with the numerical solution.Finally,effects of different parameters on amplitude-frequency curve and force transmissibility were analyzed.The results showed that the analytical solution agrees well with the numerical solution;in dimensionless case,fractional-order term coefficient,nonlinear parameters,number of fractional-order and damping ratio within resonance area can have suppressing action on resonance peaks of amplitude-frequency curve and force transmissibility;parameters within different frequency ranges can have different influences on vibration isolation effect,within lower frequency vibration isolation region,the smaller the nonlinear parameters and amplitude,the better the vibration isolation effect;damping ratio has little effect on force transmissibility;within higher frequency vibration isolation region,increasing nonlinear parameters,amplitude and damping ratio can be helpful to improve vibration isolation effect.
作者
唐建花
李向红
王敏
申永军
李壮壮
TANG Jianhua;LI Xianghong;WANG Min;SHEN Yongjun;LI Zhuangzhuang(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Lab of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2022年第1期10-18,共9页
Journal of Vibration and Shock
基金
国家自然科学基金(12172233,11672191,11772206,U1934201)
河北省高校百名人才支持计划(SLRC2017053)。
作者简介
第一作者:唐建花,女,硕士生,1993年生;通信作者:李向红,女,博士,教授,1974年生。
