Analysis of fractional element of viscoelastic fluids using Heaviside operational calculus
Fractional element model describes a special kind of viscoelastic uids. Its stress is propor- tional to the fractional-order derivatives of strain. Physically the mechanical analogues of fractional elements can be represented by self-similarity spring-dashpot fractal networks. In this paper we introduce a constitutive operator in the constitutive equations of viscoelastic uids. To derive constitutive operators for self-similarity spring-dashpot fractal networks we use Heaviside fractional calculus, which provides explicit answers not otherwise obtainable as simple. Then a con- stitutive equation of fractional element with 1/2-order derivative was derived. Finally we find the way to derive the constitutive equation with other fractional-order derivatives and its physical analogy.
viscoelastic uids Heaviside operational calculus fractional element fractional-order derivative
K.Q.Zhu K.X.Hu D.Yang
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
国际会议
The Fifth International Conference on Fluid Mechanics(第五届国际流体力学会议)
上海
英文
2007-08-15（万方平台首次上网日期，不代表论文的发表时间）