The Viscoelastic Solid Model with Fractional Order Derivative and Its Applications

The viscoelastic solid model with fractional order derivative is proposed in this paper. From the definition of fractional order derivative, the new idea that replaces the traditional Newton dashpot with Abel dashpot is also proposed . The standard linear body with fractional order derivative can successfully describe the relaxation and creep phenomenon of real material. The Stieltjes convolution of relaxation modulus and creep compliance is Heaviside unite step function strictly. The standard linear body with fractional order derivative can be satisfied with experiments of storage modulus and loss modulus of real material in very width frequency. It has extensive application foreground in the theory of viscoelastic.