A Fractional Derivative Viscoelastic Model for Hybrid Active-Passive Damping Treatments in Time Domain

Abstract

This work presents a finite element formulation for the dynamic transient analysis of a damped adaptive sandwich beam composed of a viscoelastic core and elastic-piezoelectric laminated faces. The latter are modeled using the classical laminate theory, which takes the electromechanical coupling into account by modifying the stiffness of the piezoelectric layers. For the core, a fractional derivative model is used to characterize its viscoelastic behavior. Equations of motion are solved using a direct time integration method based on the Newmark scheme in conjunction with the Grunwald approximation of fractional derivatives. Emphasis is given to the finite element implementation of the fractional derivative model and to the influence of the electromechanical coupling.

Keywords

hybrid piezoelectric-viscoelastic damping treatment fractional derivatives sandwich beam finite element method transient dynamic analysis

Get full access to this article

View all access options for this article.

References

Bagley, R.L. and Torvik, P.J. 1983. “Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped Structures,” AIAA Journal, 21: 741-748 .

Baz, A. 1997. “Boundary Control of Beams Using Active Constrained Layer Damping,” Journal of Vibration and Acoustics, 119: 166-172 .

Benjeddou, A. and Deu J.-F. 2001. “Piezoelectric Transverse Shear Actuation and Sensing of Plates, Part 1: A Three-dimensional Mixed State Space Formulation,” Journal of Intelligent Material Systems and Structures, 12: 435-449 .

Deu, J.-F. and Benjeddou, A. 2002. “Exact Free-vibration Analysis of Laminated Plates with Embedded Piezoelectric Transverse Shear Actuators or Sensors,” In: Proc. Fifth World Congress on Computational Mechanics, Mang, H.A., Rammerstorfer, F.G. and Eberhardsteiner, J. Publishers, Vienna, Austria.

Galucio, A.C. , Deu, J.-F. and Ohayon, R. 2004. “Finite Element Formulation of Viscoelastic Sandwich Beams using Fractional Derivative Operators,” Computational Mechanics, 33: 282-291 .

Golla, D.F. and Hughes, P.C. 1985. “Dynamics of Viscoelastic Structures - A Time-domain, Finite Element Formulation,” Journal of Applied Mechanics, 52: 897-906 .

Lesieutre, G.A. and Lee, U. 1996. “A Finite Element for Beams Having Segmented Active Constrained Layers with Frequency-dependent Viscoelastics,” Smart Materials and Structures, 5: 615-627 .

Pritz, T. 1996. “Analysis of Four-parameter Fractional Derivative Model of Real Solid Materials,” Journal of Sound and Vibration, 195: 103-115 .

Schmidt, A. and Gaul, L. 2001. “FE Implementation of Viscoelastic Constitutive Stress-strain Relations Involving Fractional Time Derivatives,” In: Proc. Constitutive Models for Rubbers II, A.A. Balkema, Publishers, Tokyo, Japan, pp. 79-89 .

10.

Trindade, M.A. , Benjeddou, A. and Ohayon, R. 2001. “Finite Element Modelling of Hybrid Active-passive Vibration Damping of Multilayer Piezoelectric Sandwich Beams - Part I: Formulation; Part II: System Analysis,” International Journal for Numerical Methods in Engineering, 51: 835-864 .

11.

Yi, S. and Sze, K.Y. 2000. “A Finite Element Formulation for Composite Laminates with Smart Constrained Layer Damping,” Advances in Engineering Software, 31: 529-537 .

12.

Zhang, X.D. and Sun, C.T. 1996. “Formulation of an Adaptive Sandwich Beam,” Smart Materials and Structures, 5: 814-823 .

A Fractional Derivative Viscoelastic Model for Hybrid Active-Passive Damping Treatments in Time Domain - Application to Sandwich Beams

Abstract

Keywords

Get full access to this article

References