Dr' salim Belouettar

1
Task 2.3 Models validations (UM-LPMM,
CRPHT)Interaction with EADS
Shell finite element and Numerical Algorithm for
vibrations of viscoelastic structures
2
Geometry and hypothesis
? Classical laminate theory is used.
? Elastic layers are modeled with Love Kirchhoff
assumptions.
? Reissner/Mindlin theory is used to account of
the shear deformation in the viscoelastic layer.
? No slips occurs at the interfaces between
layers. ? Materials are linear, homogeneous and
isotropic. ? All points of the elastic layers on
a normal have the same rotations.
3
Sandwich finite element obtained
A triangular sandwich finite element 8 d.o.f /
node Longitudinal displacements of faces,
rotations and deflection
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Algorithms for complex eigenvalue problem
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Principle of algorithms developed Continuation
algorithm
(K (p) - w2 M) U 0 , K (w)
K(0)E(w)N
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Validation (simple model of viscoelasticity)

• Abaqus simulation uses volume elements and MSEC.
• Eve simulation using our shell element ANM.

Complex modulus
Real modulus
Free vibrations 4 first bending modes
Damped vibrations, h1 4 first bending modes
7
Modeling of the experimental sample.

• Characteristic of the viscoelastic material 3M
  ISD 112

• - Nomograph not precise enough to extract
  reliable Pronys series.
• Value of the Youngs relaxed modulus largely
  varying in literature. ( from 0.135Mpa 1 to
  1.5MPa 2)

We used a model of ISD 112 at 27 C to illustrate
the capabilities from our element.
1 Influences of Higher Order Modeling
Techniques on the Analysis of Layered
Viscoelastic Damping Treatments. Austin M. Thesis
1998. 2 Modeling of Frequency-Dependent
Viscoelastic Materials for Active-Passive
Vibration Damping. Trindade M.A., Benjeddou A.,
Ohayon R. I.J.V.A 2000
8
Maxwells or ADF Model (Trindade, 2000)
Comparison of numerical results (Abaqus, Eve).
Damped vibrations, Maxwell or ADF model, 4 first
bending modes
9
WP2 Task 2.1 Dissemination
CRPHT , UM-LPMM H.Hu, S. Belouettar, E.M. Daya
and M. Potier-Ferry, Evaluation of kinematics
formulations for viscoelastically damped sandwich
beams Journal of Sandwich Structures and
Materials, Accepted