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Model Validation for Vibrations of Viscoelastic Structures Using Finite Element and Numerical Algorithms

This research focuses on validating vibration models of viscoelastic structures through finite element methods and numerical algorithms. Classical laminate theory, Love Kirchhoff assumptions, and Reissner/Mindlin theory are utilized. A sandwich finite element with 8 degrees of freedom per node is developed, considering longitudinal displacements, rotations, and deflections. Various algorithms, such as the QR method, asymptotic approach, and iterative techniques, are explored for complex eigenvalue problems. The study includes the modeling of a viscoelastic sample, showcasing the capabilities of the developed element with applications in damped vibrations and modal analysis. The research also discusses the challenges in modeling viscoelastic materials and compares numerical results using different models. The validation process involves Abaqus simulations, ANM algorithms, and evaluation of Maxwell or ADF models. Continuation algorithms and homotopy techniques are utilized for accurate model validation.

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Model Validation for Vibrations of Viscoelastic Structures Using Finite Element and Numerical Algorithms

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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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