43 A General Framework for Time Domain Finite Element Analysis of Viscoelastically Damped Structures 385 Fig. 43.2 Time response of the sandwich beam for each viscoelastic model implemented 43.4 Conclusions A general framework for the computation of time responses of viscoelastically damped systems was proposed in this work, by using two-step recurrence formulas involving internal variables in the time discretisation scheme. The generalised Maxwell model, the anelastic displacement field model, the Golla-Hughes-McTavish model and a four-parameter fractional derivative model were implemented within a modified Newmark scheme to compute the time response of sandwich structures subjected to a transient load. It is shown that by identifying properly the models’ parameters, the results obtained with each models are similar. These results prove the effectiveness of the proposed methodology. The evolution of the error in amplitude and in period needs to be investigated further, as well as the order of convergence of numerical schemes. References 1. Golla, D.F., Hughes, P.C.: Dynamics of viscoelastic structures – a time domain finite formulation. J. Appl. Mech. 52, 897–906 (1985) 2. Lesieutre, G.A., Bianchini, E.: Time domain modeling of linear viscoelastic using anelastic displacement fields. J. Vib. Acoust. 117, 424–430 (1995) 3. Bagley, R.L., Torvik, P.J.: A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27, 201–210 (1983) 4. Vasques, C.M.A., Moreira, R.A.S., Dias Rodrigues, J.: Viscoelastic damping technologies – part I: modeling and finite element implementation. J. Adv. Res. Mech. Eng. 1, 76–95 (2010) 5. Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, Beijing (1998) 6. Galucio, A.C., Deü, J.-F., Ohayon, R.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comput. Mech. 33, 282–291 (2004)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==