Dynamic Finite Element analysis of fractionally damped structural systems in the time domain

1. Bathe K.J.: Finite Element Procedures. Prentice Hall, Englewood Cliffs (1996)

   Google Scholar 

2. Bucher C., Wolff S.: slangTNG—scriptable software for stochastic structural analysis. In: DerKiureghian, A., Hajian, A. Reliability and Optimization of Structural Systems, pp. 49–56. American University of Armenia Press, Oakland (2013)

   Google Scholar 

3. Cataldo, E., Di Lorenzo, S., Fiore, V., Pirrotta, A., Valenza, A.: Bending test for capturing the fractional visco-elastic parameters: theoretical and experimental investigation on giant reeds. In: International Conference on Fractional Differentiation and its Applications. doi:10.1109/ICFDA.2014.6967408 (2014)

4. Christensen R.M.: Theory of Viscoelasticity: An Introduction. Academic Press, Waltham (1982)

   Google Scholar 

5. Cortés F., Elejabarrieta M.J.: Finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models. Int. J. Numer. Methods Eng. 69, 2173–2195 (2007)

   Article  MATH  Google Scholar 

6. Di Lorenzo, S., Pinnola, F.P., Pirrotta, A.: On the dynamics of fractional visco-elastic beams. In: Proceedings of the ASME 2012 Intermational Mechanical Engineering Congress and Exposition IMECE2012 (2012)

7. Di Paola M., Pirrotta A., Valenza A.: Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech. Mater. 43, 799–806 (2011)

   Article  Google Scholar 

8. Diethelm K., Ford N.J., Freed A.D., Luchko Y.: Algorithms for the fractional calculus; a selection of numerical methods. Comput. Methods Appl. Mech. Eng. 194, 743–773 (2005)

   Article  MATH  MathSciNet  Google Scholar 

9. Flügge W.: Viscoelasticity. Blaisdell Publishing Company, Massachussetts (1967)

   Google Scholar 

10. Gemant, A.: A method of analyzing experimental results obtained by elasto-viscous bodies. Physics, 7(8), 311–317 (1936)

11. Katsikadelis J.T.: Numerical solution of multi-term fractional differential equations. ZAMM 89(7), 593–608 (2009)

    Article  MATH  MathSciNet  Google Scholar 

12. Katsikadelis J.T.: The BEM for numerical solution of partial fractional differential equations. Comput. Math. Appl. 62, 891–901 (2011)

    Article  MATH  MathSciNet  Google Scholar 

13. Müller S., Kästner M., Brommund J., Ulbricht V.: On the numerical handling of fractional viscoelastic material models in a fe analysis. Comput. Mech. 51, 999–1012 (2013)

    Article  MATH  MathSciNet  Google Scholar 

14. Nerantzaki M.S., Babouskos N.G.: Vibrations of inhomogeneous anisotropic viscoelastic bodies described with fractional derivative models. Eng. Anal. Bound. Elem. 36, 1894–1907 (2012)

    Article  MathSciNet  Google Scholar 

15. Nutting P.G.: A new general law of deformation. J. Franklin Inst. 191, 678–685 (1921)

    Article  Google Scholar 

16. Pipkin A.: Lectures on Viscoelasticity Theory. Springer, Berlin (1972)

    Book  MATH  Google Scholar 

17. Pirrotta A., Cutrona S., Di Lorenzo S.: Fractional visco-elastic timoshenko beam from elastic euler–bernoulli beam. Acta Mech. 226, 179–189 (2015)

    Article  MATH  MathSciNet  Google Scholar 

18. Przemieniecki J.S.: Theory of Matrix Structural Analysis. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

19. Samko S.G., Kilbas A.A., Marichev O.I.: Fractional Integrals and Derivatives—Theory and Applications. Gordon and Breach Science Publishers, New York (1993)

    MATH  Google Scholar 

20. Schmidt A., Gaul L.: Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dyn. 29, 37–55 (2002)

    Article  MATH  Google Scholar 

21. Spanos P.D., Evangelatos G.I.: Response of a non-linear system with restoring forces governed by fractional derivatives—time domain simulation and statistical linearization solution. Soil Dyn. Earthq. Eng. 30, 811–821 (2010)

    Article  Google Scholar 

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