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分数导数模型能涵盖标准机械模型,并能够比较精确地描述粘弹性材料本构关系。该文对一种橡胶材料进行了不同温度和不同应变幅值下的频率扫描实验,得到了橡胶材料的储能模量、损耗模量和损耗因子随频率的变化情况。分别采用分数阶Kelvin-Voigt模型和高阶分数导数FVMP模型(fraction Voigt and Maxwell model in parallel)预测该材料的频率响应曲线,对橡胶材料动态力学性能进行评估。与实验结果的对比分析表明:分数阶Kelvin-Voigt模型存在一定的误差,而高阶分数导数FVMP模型能较好地描述该材料在不同温度和不同应变幅值下的动态力学行为。
Fractional derivative model can cover the standard mechanical model, and can more accurately describe the viscoelastic material constitutive relationship. In this paper, the frequency scanning experiment of a rubber material under different temperatures and different strain amplitudes was carried out. The storage modulus, loss modulus and loss factor of the rubber material were obtained with frequency. The fractional Kelvin-Voigt model and the FVMP (fractional high-order fractional derivative) FVMP model were used to predict the frequency response of the material. The dynamic mechanical properties of the rubber material were evaluated. The experimental results show that fractional Kelvin-Voigt model has some errors, while the high-order fractional derivative FVMP model can describe the dynamic behavior of the material at different temperatures and different strain amplitudes.