Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

By A. Galucio, Jean-François Deü, R. Ohayon. 2004

269 citations recorded by the source corpus.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler–Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e32a8b30fd86e94c8a322e7e6168508cd30a9cac

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In Civil and Structural Engineering

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations (2010, methodology): “[9] presented a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations.”
Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods (2009, methodology): “ε11 denotes the axial strain, and ε22 denotes the strain in transverse direction, which has often been ignored in previous work [12].”
Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers (2010, unknown): “However, fractional models of which the parameters are real numbers are also proposed, for example, in [10,21,22].”