Fractional Order Integral Models And Numerical Methods Of Several Kinds Viscoelastic Material

Many researchers have found that a lot of materials not only have viscous or elastic character-istics but is closed to viscoelastic characteristics. The result of integer-order viscoelastic model is accurate and realistic than the viscous or elastic model. With the fractional calculus more and more attention, the study found that integer order viscoelastic model still can’t meet the actual needs, but fractional order viscoelastic model is more accurate, more in line with the actual situation. Therefore, the paper consider the establishment of fractional integral model and seek the numerical solution of fractional integral.This paper is divided into six chapters.In Chapter1, brief statement of paper research background, significance and research status are given. In Chapter2, the definition and operational properties of fractional calculus, the relaxation modulus and creep modulus of several kinds fractional order viscoelastic model are briefly intro-duced.In Chapter3, fractional order model of Burgers was introduced to describe the creep or respond behavior. Then using the power function of creep compliance to establish fractional integral model and the numerical solution of strain is obtained.In Chapter4, according to the one-dimensional viscoelastic constitutive relationship, we set up fractional differential model about seismic wave. Then base on the definition of fractional order calculus we obtain fractional integral equation model. Complex rectangular numerical approximation and Chebyshev polynomial approximation are used to solve this integral equation. The plane wave is applied to calculate quality factor-Q and comparison of numerical solutions is made.In Chapter5, according to the constitutive equation of Stokes’ second problems, we obtain fractional integral equation model. The fractional order and two-dimensional differential transfor-m method are used to solve integral equation. And the result is compared with the exact solution of Newtonian fluid.In Chapter6, the main work done by the paper is summarized and the future outlook of the work is proposed.