Modeling and dynamic analysis of fractional order nonlinear viscoelastic rod

A fractional order constitutive behavior law is proposed in this paper to describe the viscoelasticity of the nonlinear rod. The fractional governing equation of the nonlinear viscoelastic rod is established. An effective algorithm based on the shifted Legendre polynomials is used to solve the governing equation directly in the time domain. The effectiveness of the proposed numerical algorithm is confirmed by the convergence analysis. Its accuracy is verified by the comparison with the analytical solution of a dimensionless equation. The dynamic response of the viscoelastic rod under various loading conditions is analyzed. The influence of loading parameters on the dynamic characteristics of the rod is investigated according to the evolution of displacement and stress.