以经典Kelvin分数导数理论为基础,建立新型BTG塑料合金的改进Kelvin分数导数动态本构模型,该模型综合描述了温度、频率和振幅与BTG塑料合金模量的关系.通过动态热分析仪DMA242,获取了BTG塑料合金几个温度下,振幅恒为30μm时的频率扫描和几个频率下的恒温幅值扫描的动态存储模量和损耗模量实验数据.首先分析频率扫描实验数据,识别出各温度下的改进分数导数模型的系数,然后研究这些系数关于温度的变化规律,以此建立了温度频率模型.其次分析幅值扫描数据,发现不同频率的各实验振幅的模量与各自振幅30μm的模量比值相等,所以建立了模量比值关于振幅的函数模型.将温度频率模型与模量比值振幅模型相乘就建立了综合考虑温度-频率-振幅的动态本构关系.建立的综合考虑温度-频率-振幅的本构模型能准确表达实验数据.结果表明：改进的综合考虑温度、频率和振幅的分数导数动态本构模型真确合理,该模型适合于BTG塑料合金的动态模量变化规律的描述.
We established dynamic model of modified Kelvin fractional derivative for a new type of plastic alloy BTG based on the classical Kelvin fractional derivative theory.This model describes the modulus of plastic alloy BTG affected by temperature,frequency and amplitude.The experimental data of the storage modulus and loss modulus of the frequency sweep under conditions of constant amplitude 30 μm for several temperatures and amplitude scanning under conditions of constant temperature for several frequency were obtained first,and then the temperature-frequency model and the function model of modulus ratio about amplitude was set up,finally,the dynamic constitutive model about the temperature,frequency and amplitude was presented by the product of temperature-frequency model and function model of modulus ratio.The results show that the dynamic model of modified Kelvin fractional derivative is true and suitable to express the dynamic modulus of plastic alloy BTG.
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