基于分数阶导数的黏弹性减振系统时频特性

Time and Frequency Features of Viscoelastic Vibration Damping System Based on Fractional Derivative

黏弹性减振缓冲结构可抽象为黏弹性振子(VEO)来研究其动力学行为.提出了构建考虑几何系数的分数阶黏弹性振子(FVEO)模型的一般方法.以Kelvin-Voigt分数阶黏弹性振子(KFVEO)系统为例,采用拉普拉斯变换得到其频率特征函数,并利用Mellin-Fourier积分将KFVEO系统响应从复频域转化到时域,采用多值函数的复变积分原理和留数定理获得KFVEO系统时间历程的解析形式.以安装在某300k W履带拖拉机的黏弹性悬架为工程应用实例,应用所提模型在时频域分析了其翻越障碍时应对冲击振动的减振缓冲性能,以及分数阶数和几何参数的影响.结果表明,该悬架具有良好的减振性能,在频率比0.8238处出现振动峰值;几何参数与分数阶数均对减振效果有明显影响.为复杂黏弹性缓冲减振结构的精确建模和参数化设计提供相应的理论依据.

Viscoelastic structure can be abstracted dynamic behavior. The generalized modeling out viscoelastic oscillator （VEO） to research its of fractional VEO （FVEO） involving geometric factors was proposed. Take the KFVEO as the research case and its frequency features were obtained through Laplace transform. Mellin-Fourier integral was adopted to transform response from frequency domain to time domain, based on which the time history in analytical form was derived by complex integral and residue theorem for multivalued function. For engineering application,the viscoelastic suspension installed in a 300kW crawler vehicle was studied by simplifying to KFVEO and its vibration control capability and coefficient effect for climbing over an obstacle were analyzed through the proposed fractional order model. The results show that the viscoelastic suspension exhibits considerable vibration damping capability, and vibration peak occurs at frequency ratio 0. 8238;Geometric factor and fractional order exert distinct effects on the vibration control. This study can offer theoretical basis for accurate modeling and parametric design of complex viscoelastic structures.