A Numerical Method for Solving Fractional-Order Viscoelastic Euler-Bernoulli Beams

This is the accepted version of the following article: "A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams", which has been published in final form at https://www.sciencedirect.com/science/article/pii/S0960077919302863International audienceIn this paper, a new method is presented for solving the constitutive equations of fractional-order viscoelastic Euler-Bernoulli beams. Firstly, the constitutive equation of the Euler-Bernoulli beam is established by analyzing the constitutive relation between the fractional viscoelastic materials. Secondly, the constitutive equation of the beam is transformed into a matrix equation by using a Quasi-Legendre polynomial in the time domain. Then the matrix equation is discretized and solved, and the numerical solution is obtained for the constitutive equation of the beam. Finally, numerical analysis of two different fractional viscoelastic materials is carried out by numerical experiments. Displacements under different external loads are obtained for the polybutadiene beam and butyl B252 beam. With the change of time and position, the change law of displacements is found. And the performance of the two materials is compared and analyzed