摘要
A Fractional element model describes a special kind of viscoelastic material. Its stress is proportional to the fractional-order derivative of strain. Physically the mechanical analogies of fractional elements can be represented by spring-dashpot fractal networks. We introduce a constitutive operator in the constitutive equations of viscoelastic materials. To derive constitutive operators for spring-dashpot fractal networks, we use Heaviside operational calculus, which provides explicit answers not otherwise obtainable simply. Then the series-parallel formulas for the constitutive operator are derived. Using these formulas, a constitutive equation of fractional element with 1/2-order derivative is obtained. Finally we find the way to derive the constitutive equations with other fractional-order derivatives and their mechanical analogies.
A Fractional element model describes a special kind of viscoelastic material. Its stress is proportional to the fractional-order derivative of strain. Physically the mechanical analogies of fractional elements can be represented by spring-dashpot fractal networks. We introduce a constitutive operator in the constitutive equations of viscoelastic materials. To derive constitutive operators for spring-dashpot fractal networks, we use Heaviside operational calculus, which provides explicit answers not otherwise obtainable simply. Then the series-parallel formulas for the constitutive operator are derived. Using these formulas, a constitutive equation of fractional element with 1/2-order derivative is obtained. Finally we find the way to derive the constitutive equations with other fractional-order derivatives and their mechanical analogies.
基金
Supported by the National Natural Science Foundation of China under Grant No 10972117.
