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Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model

Author

Listed:
  • Mikel Brun

    (Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain)

  • Fernando Cortés

    (Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain)

  • María Jesús Elejabarrieta

    (Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain)

Abstract

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction.

Suggested Citation

  • Mikel Brun & Fernando Cortés & María Jesús Elejabarrieta, 2021. "Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model," Mathematics, MDPI, vol. 9(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1731-:d:599357
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    References listed on IDEAS

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    1. Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
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    Cited by:

    1. Michael R. Booty, 2023. "Preface to the Special Issue on “Computational Mechanics in Engineering Mathematics”," Mathematics, MDPI, vol. 11(3), pages 1-3, February.

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