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Task 2.3 : Models validations (UM-LPMM, CRPHT) Interaction with EADS

Task 2.3 : Models validations (UM-LPMM, CRPHT) Interaction with EADS. Shell finite element and Numerical Algorithm for vibrations of viscoelastic structures. z. he1. elastic. hv. viscoelastic. x. elastic. he2. Geometry and hypothesis.  Classical laminate theory is used.

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Task 2.3 : Models validations (UM-LPMM, CRPHT) Interaction with EADS

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  1. Task 2.3 : Models validations (UM-LPMM, CRPHT)Interaction with EADS Shell finite element and Numerical Algorithm for vibrations of viscoelastic structures

  2. z he1 elastic hv viscoelastic x elastic he2 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

  4. ([K (w)] - w2 [M]) [U] = 0 U :complex eigenmode w2 :complex eigenvalue - Constant complex modulus - Low damping -QR method -Asymptotic approach (Ma et He 1992) • -Iterative algorithm (Chen et al. 1999) • Algorithms developed at LPMM • - Continuation algorithm(Computer & Structures, 2001) • - Iterative algorithms(2003) Algorithms for complex eigenvalue problem

  5. Homotopy technique ([K(0)] +  E(p)[N]+p2 [M]) [u] =0 0  1 • Asymptotic Numerical Method. U and p are searched as a truncated integer - power series with respect to  • Continuation procedure While   1 next stepof ANM is needed Set of recrrent linear problems with the same matrix Principle of algorithms developed Continuation algorithm ([K (p)] - w2 [M]) [U] = 0 , [K (w)] =[K(0)]+E(w)[N]

  6. *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, h=1 4 first bending modes

  7. *Modeling of the experimentalsample. • Characteristic of the viscoelastic material: 3M ISD 112 • - Nomograph not precise enough to extract reliable Prony’s series. • Value of the Young’s 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. *Maxwell’s 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

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