介电松弛的基本分数模型及其在频率域上的松弛特征

分数阶动力学方程从本质上讲具有耗散性质,对力学黏弹过程的描述取得了成功的应用.本文介绍了介电松弛的基本分数单元——容阻器,利用容阻器建立了介电松弛的基本分数模型,给出了各模型的本构方程和复介电常数,分析对比了它们的松弛特性.结果表明分数模型可以给出丰富的具有不同频率特性的松弛过程,如Cole-Cole方程可以作为分数模型的特例给出.本文还用分数Poynting-Thomson模型对丙三醇的介电松弛行为进行了拟合,对介电常数与介电损耗都给出了很好的描述.

The fractional models for dielectric relaxation and their relaxation characteristics in frequency domain

The dynamic process represented by the fractional calculus is in nature dissipative, and the fractional constitutive equations have been successfully applied in describing the viscoelastic phenomena. In this paper, the fractional element for the dielectric relaxation, the ＂cap-resistor＂, is introduced, and the basic fractional models of dielectric relaxation are constructed. The constitutive equations of the fractional models are derived, and their complex permittivities are presented. Analysis on the relaxation characteristics shows that these fractional models can offer relaxation processes with diverse frequency dependence, and some classical models such as Cole-Cole equation can be regarded as a special case of the fractional model. In addition, the fractional Poynting-Thomson model is used to simulate the dielectric relaxation behavior of glycerol, the fitting results show the model can delineate the dielectric constant and the dielectric loss very well.