A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

This paper presents a new numerical method to solve the constitutive equations of fractional-order viscoelastic Euler–Bernoulli beams. Firstly, the constitutive equation of Euler–Bernoulli beams is established by analyzing the constitutive relation between the fractional viscoelastic materials. Secondly, the constitutive equation of the beams is transformed into a matrix equation by skillfully using a Quasi-Legendre polynomial in the time domain, which can greatly simplify the solution process. Then the matrix equation is discretized and solved, and the numerical solutions are obtained. Finally, dynamic analysis of two different fractional viscoelastic materials is carried out by numerical experiments, and the influences of time on displacements are considered for the first time. With the change of time and position, displacements under different external loads are obtained for the polybutadiene beams and butyl B252 beams, and the change law of displacements is found. In addition, the performances of the two materials are compared and analyzed.