Numerical calculating linear vibrations of third order systems involving fractional operators

Abstract

This paper presention a numerical method for dynamic colculation of third order systems involving fractlonal operators. Using the Liouville-Rieman’s definition of fractional derivatives, a numerical algorithm is developed on base of the well-known New-mark integration method to calculate dynamic response of third order systems. Then, we apply this method to calculate linear vibrations of viscoelastic systems containing fractional derivatives.