A viscoelastic Timoshenko Beam Model: Regularity and Numerical Approximation

We derive a fully-discrete finite element scheme to a fractional Timoshenko beam model, which characterizes the mechanical responses of viscoelastic beams, thick beams and beams subject to high-frequency excitations by properly considering the effects of both transverse shear and rotational inertia. We prove high-order regularity of the solutions to the model and then accordingly prove error estimates of the numerical scheme. Numerical experiments are performed to substantiate the numerical analysis results and to demonstrate the effectiveness of the fractional Timoshenko beam model in modeling the mechanical vibrations of different beams, in comparison with its integer-order analogue and the widely-used integer-order and fractional Euler-Bernoulli beam models.