一种磁流变阻尼器的分数阶微分模型

Fractional differential model of a type of magnetorheological damper

对磁流变阻尼器系统建立分数阶微分方程表征其非线性特征,将系统输出位移信号拟合磁流变阻尼器系统分数阶微分方程,以4个参数拟合这一黏弹性系统,其拟合精度明显高于整数阶微分方程。实验和分析表明,微分方程的阶数与磁流变阻尼器加载的电流有关,加电流时分数阶项阶数较不加电流时明显升高;加电流后分数阶项的阶数随电流强度的增加而增大;同时电流强度越大,系统惯性力的影响越小,黏、弹性力的影响程度也发生变化,控制电流强度越大,黏性力的影响越占优势;当磁流变液达到磁饱和时,模型不再随电流强度的变化发生改变。系统的黏弹特性和系统模型参数也受磁流变液性能和工作条件的影响。

A fractional differential equation that needs only 4 parameters is matched using displacement signals to describe the nonlinearity of MRF damping system. It is demonstrated that the control currents will exert a significant influence on the order of the fractional system. Compared with the condition where no magnetic field exists, the order of the system is higher and increasing with the applied currents, while the influence of the inertia decreases. The visco-elasticity of the system and the parameters of the FOS also depend on the performance of the MRF.