Damping and Forced Vibration Analyses of a Piezoelectric/Elastic/Viscoelastic/Elastic/Piezoelectric Structures

Abstract:

A mathematical model for the forced vibration of sandwich structures with a viscoelastic and piezoelectric layers is presented. The active-passive damping is realized by adding piezoelectric sensor and actuator layers to a sandwich viscoelastic structure. The mathematical formulation is developed in a general form in order to take into account for various viscoelastic models in the frequency domain. Frequency dependent Young modulus based on various Maxwells model is used for viscoelastic materials modelling. A numerical method combining the finite element and perturbation methods called asymptotic numerical method is developed for the displacement and frequency dependent problem. Resonance curves for sandwich structures are obtained for various frequency ranges, excitation amplitudes and viscoelastic models. Only some matrix inversions and a few iterations are needed for large frequency ranges.

• Periodical: Advanced Materials Research (Volume 682)
• Pages: 1-8
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.682.1
• Online since: April 2013
• Authors: F. Abdoun, L. Azrar, E.M. Daya
• Keywords: Finite Element Method (FEM), Forced Vibration, Frequency Response, Piezoelectric, Sandwich Structure, Viscoelastic

References

[1] ML. Soni: Finite element analysis of viscoelastically damped sandwich structures. Shock Vib Bull,55(1) (1981), 97–109.

[2] F. Abdoun, L. Azrar and E.M. Daya: Damping and forced vibration analyses of viscoelastic shells. International Journal for Computational Methods in Engineering Science and Mechanics, 11(2) (2010), 109–122.

DOI: 10.1080/15502280903563533

[3] F. Abdoun, L. Azrar, E.M. Daya and M. Potier-Ferry: Forced vibrations of sandwich viscoelastic beams and plates by an Asymptotic Numerical Method. Computers & Structures, 87(1-2) (2009), 91-100.

DOI: 10.1016/j.compstruc.2008.08.006

[4] E.M. Daya and M. Potier-Ferry: A numerical method for nonlinear eigenvalue problem, application to vibrations of viscoelastic structures. Computers &Structures; 79(5) (2001), 533–41

DOI: 10.1016/s0045-7949(00)00151-6

[5] B.A. Ma and J.F. He: Finite element analysis of viscoelastically damped sandwich plates. Journal of Sound and Vibration, 52(1992), 107–123.

DOI: 10.1016/0022-460x(92)90068-9

[6] D.K. Rao: Frequency and loss factor of sandwich beams under various boundary conditions. Journal of Mechanical Engineering Science, 20(5) (1978), 271–282.

DOI: 10.1243/jmes_jour_1978_020_047_02

[7] A. Benjeddou: Advances in hybrid active-passive vibration and noise control via piezoelectric and viscoelastic constrained layer treatments. J. Vib. Control,7(4) 2001,565–602.

DOI: 10.1177/107754630100700406

[8] H. Boudaoud, S. Belouettar, E.M. Daya, M. Potier-Ferry: A shell element for active-passive vibration control of composite structures with piezoelectric and viscoelastic layers, Mechanics of Advanced Materials and Structures, 15(2008), 208–219.

DOI: 10.1080/15376490801907699

[9] A. Benjeddou, M. A. Trindade and R. Ohayon: A unified beam finite element model for extension and shear piezoelectric actuation mechanisms. J. Intell. Mater. Syst. Struct. 8 1012 (1997).

DOI: 10.1177/1045389x9700801202

[10] S.S. Rao and M. Sunar: Piezoelectricity and its use in disturbance sensing and control of flexible structures: A survey. Appl. Mech. Rev. 47 (4) (1994), 113–123.

DOI: 10.1115/1.3111074

[11] M. Sunar, S.S. Rao: Recent advances in sensing and control of flexible structures via piezoelectric materials technology. Appl. Mech. Rev. 52 (1) (1999), 1–16.

DOI: 10.1115/1.3098923