A factional-order derivative model of the magnetorheological damping system was addressed, an analytical solution and an effective numerical solution of the model were given. The displacements in different currents were adopted here to study the nonlinear characteristics of the damping system. Experiments show that fractional-order derivative model is more precise than integer-order derivative model of the transfer function, and the nonlinear characteristics of the damping system are related to the fractional orders. And the orders are associated with the control currents of the damping system. It is indicated the model of fractional-order derivative is feasible and effective for investigation of magnetorheological vibration device. 

建立了磁流变减振系统的分数阶导数模型，并求出了该模型的解析解和数值解。在不同控制电流下，基于系统振幅的变化研究了磁流变振动装置的非线性特征，探讨了分数阶导数在磁流变控制系统中的应用。实验证明：采用分数阶导数的系统模型较之采用整数导数的系统模型更精确，减振系统的非线性特性跟分数阶导数算子的阶数有关，分数阶导数算子的阶数与减振系统的控制电流有关。结果表明，分数阶导数模型在磁流变阻尼器的减振模型上是有效的。

 

磁流变液, 分数阶导数, 减振系统, 非线性特征