广义分数阶van der Pol-Duffing振子的动力学响应与隔振效果研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (1) : 10-18.

论文

唐建花1,李向红1,3,王敏1,申永军2,3,李壮壮2

作者信息 +

Dynamic response and vibration isolation effect of generalized fractional-order van der Pol-Duffing oscillator

TANG Jianhua1, LI Xianghong1,3, WANG Min1, SHEN Yongjun2,3, LI Zhuangzhuang2

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文章历史 +

摘要

本文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。首先, 我们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。最后, 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。

Abstract

By means of the average method, this paper studied the dynamic behavior and force transmissibility of the van der Pol-Duffing oscillator with fractional derivative term. First, the first-order analytical solution of the van der Pol-Duffing oscillator with fractional derivative term was calculated. Further, the expressions of the amplitude-frequency curve and the phase-frequency curve for the steady solution were obtained. The correctness of the analytical solution was verified by comparing with the numerical solution. Finally, the influence of different parameters on the amplitude-frequency curve and the force transmissibility was analyzed. The results show that, the analytical solution is in good agreement with numerical solution. In the dimensionless case, some parameters can restrain the resonance peaks of the amplitude-frequency curve and the force transmissibility within the resonance region, such as the fractional order coefficients, nonlinear parameters, fractional order, and damping ratio. In the low-frequency vibration isolation area, the nonlinear parameters and amplitude have a significant effect on the vibration isolation effect, the smaller the nonlinear parameters and amplitude, the better the vibration isolation effect may be. In the high-frequency vibration isolation area, the increase of some parameters helps to improve the vibration isolation effect, such as the non-linear parameters, amplitude and damping ratio.

导出引用

唐建花1,李向红1,3,王敏1,申永军2,3,李壮壮2. 广义分数阶van der Pol-Duffing振子的动力学响应与隔振效果研究[J]. 振动与冲击, 2022, 41(1): 10-18

TANG Jianhua1, LI Xianghong1,3, WANG Min1, SHEN Yongjun2,3, LI Zhuangzhuang2. Dynamic response and vibration isolation effect of generalized fractional-order van der Pol-Duffing oscillator[J]. Journal of Vibration and Shock, 2022, 41(1): 10-18

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