分数导数标准线性固体粘弹性材料力学性能研究

Mechanical Properties Research on Fractional Derivative Standard Linear Solid Viscoelastic Material

分数导数粘弹性模型以及其本构理论能够比经典粘弹性模型更好地描述出粘弹性材料的力学性能.利用基于分数阶理论建立的粘弹性三参数标准线性固体模型,对粘弹性固体材料的储能柔量、耗能柔量、摩擦角、储能模量及耗能模量等性能参数进行分析,并通过数值算例探讨了粘弹性三参数标准线性固体材料部分力学性能的变化规律.研究表明:角频率和分数导数微分算子的阶数对材料的力学性能的影响较大,低频的粘弹性材料可近似看做弹性材料,而高频率的粘弹性材料在一个周期内会发生耗散现象.当角频率等于零时,材料的无量纲存储模量等于1,即粘弹性材料处于橡胶状态;当角频率逐渐增大时,材料的无量纲存储模量和耗散模量等力学性能随着分数导数的阶数的增大而逐渐增加.

Fractional derivative viscoelastic model and its constitutive theory can provide a better description for the mechanical properties of viscoelastic material than classical viscoelastic model. Based on the theory of fractional order to establish the standard linear solid model of three parameters, energy storage compliance, energy consumption compliance, friction angle, energy storage modulus and energy consumption modulus of viscoelastic solid materials were analyzed, and through the numerical examples the change rules of mechanical properties of the three parameters standard linear viscoelastic solid material were discussed. Research has shown that the effect of the angular frequency and fractional derivative order differential operator on the mechanical property of material is larger, and low frequency viscoelastic materials can be approximately viewed as elastic material, and high frequency viscoelastic material in a cycle shows the dissipation phenomenon. When the angular frequency is equal to zero, the dimensionless storage modulus of the material is equal to 1, that is, the viscoelastic material is in rubber state. When the angular frequency increases gradually, the mechanical properties of the dimensionless storage modulus and dissipation modulus of the material gradually increase with the increase of the order number of the fractional derivative.