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LPMM Contribution WP2

LPMM Contribution WP2 Shell finite element and Numerical Algorithm for vibrations of viscoelastic structures Task : 2.3, Models Validation. Position of problem. 2 elastic faces one viscoelastic core with properties depending on temperature and frequency.

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LPMM Contribution WP2

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  1. LPMM Contribution WP2 Shell finite element and Numerical Algorithm for vibrations of viscoelastic structures Task : 2.3, Models Validation

  2. Position of problem • 2 elastic faces • one viscoelastic core with properties depending on temperature and frequency Complex non linear eigenvalue problem • Objectives Frequency Determine modal properties Damping • Limitation No reliable code to determine directly modal properties Shell element + numerical method

  3. z x Uxs,Uys,Uxa,Uya W, Rx, Ry, Rz • We use a shell 3 nodes, 8 d.d.l. per node element, inspired from Bathoz and Dhatt D.K.T 18 [1] and Daya and Potier-Ferry D.K.T. 24 [2]. • Element • A shell quadrilateral element is too available to model the structure. • Kinematics hypothesis • All points on a normal to the shell have the same transverse displacement w(x,y,t) and the origine of z axis is the medium plane. • No slip occurs at the interfaces between layers. • The displacement is C0 class along the interfaces. • Elastic layers are modeled with Love Kirchhoff assumptions. • Reissner/Mindlin theory is used to account of the shear deformation in the viscoelastic layer. • The elastic and viscoelastic materials are linear, homogenous and isotropic. • For the viscoelastic core the Young's modulus is complex and depends on the vibration frequency. • The Poisson's ratio is assumed constant. • All points of the elastic and piezoelectric layers on a normal have the same rotations. [1] “Modélisation des structures par éléments finis. Coques”, Hermès, 1990. [2] “A shell finite element for viscoelastically damped sandwich Structures”, Revue Européenne des Eléments Finis, 2002, vol.11,p39-56.

  4. Numerical method The finite element formulation of the former problem lead to: As we consider the a generalized Maxwell model for the viscoelastic core the natural vibration problem became: We have here to characterize the viscoelastic layer • Storage and loss factor of material ISD112 has been measured by EADS using a viscoanalyzer. The experiments were conducted for temperatures from 0° to 100°, step 10°. • Using the obtained master curve we deduce a generalized Maxwell model.(1)

  5. Numerical Results • The viscoelastic properties of the structure have been directly obtained using EADS test performed on the ISD112. From the different experimental test we derived a Maxwell’s model. • Using the former developped shell element coupled with an asymptotic numerical method (A.N.M.) Daya and Potier-Ferry [1] we obtained directly the modal properties of the sandwich. • Using Abaqus and a direct frequency response of an harmonic excitation we obtained the frequency and damping of the system. • Comparison between the shell element result, Abaqus 3D model, and experimental results have been performed. [1] “A shell finite element for viscoelastically damped sandwich Structures”, Revue Européenne des Eléments Finis, 2002, vol.11,p39-56.

  6. Structure studied 0.8 mm 0.254 mm 1.2 mm 50 mm 300 mm

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