Finite element analysis of linear systems with fractional derivative damping models

This paper presents a method for reducing the computational effort due to finite element analysis of vibrating linear systems with fractional derivative viscoelastic models. Fractional derivative rheological models are known to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in term of modal analysis. But the growth in matrix dimensions carried by this expansion is in general so fast to make the calculations too cumbersome for finite element applications. However, according to the technique proposed in this paper, the computational effort can be taken under control by reducing the main eigenproblem of large dimension to the solution of two related eigenproblems of lower size. Numerical examples are provided in order to validate both the accuracy and the efficiency of the proposed methodology.