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Effect of crack on the dynamic response of bidirectional porous functionally graded beams on an elastic foundation based on finite element method

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Abstract

The contribution provided in this study is to investigate the dynamic response of Euler–Bernoulli imperfect FG beams-cracked on Winkler-elastic foundation, considering pinned–pinned boundary condition. The equations are discretized with classical finite element method (h-FEM). The material properties are considered vary in the both; width and thickness directions of the beam, via power-law form. An approximate porosity model with uniform distribution was adopted. The cracked element stiffness is determined based on the reduction of the cross section of the bi-directional FG beam. While the elastic foundation Winkler-type has a longitudinal distribution and increases the system stiffness. The obtained numerical results in terms of dimensionless fundamental frequencies are compared with the results from previous studies for convergence studies. Case studies were conducted to analyze the influence of power law index, porosity values, crack depth, crack location, Winkler-elastic foundation parameters on the first three natural frequencies of the beam with pinned–pinned boundary condition. The results showed that the bi-directional distribution function has a significant role in approximating the values of frequencies. The current distribution function proved its eligibility in predicting the results of the dynamic behavior of beam structures with different models distribution.

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Authors and Affiliations

  1. Laboratory of Structures, Geotechnics and Risks, Department of Planning and Hydraulic Engineering, Higher National School of Hydraulics, 9000, Blida, Algeria

    Mouloud Dahmane

  2. Department of Civil Engineering, Faculty of Civil Engineering and Architecture Engineering, Amar Telidji University, Laghouat, Algeria

    Mourad Benadouda

  3. Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Chelf, Algeria

    Riadh Bennai

  4. Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Chlef, Algeria

    Ahmed Saimi

  5. IS2M Laboratory, Faculty of Technology, University of Tlemcen, Tlemcen, Algeria

    Hassen Ait Atmane

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  1. Mouloud Dahmane
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Dahmane, M., Benadouda, M., Bennai, R. et al. Effect of crack on the dynamic response of bidirectional porous functionally graded beams on an elastic foundation based on finite element method. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03906-1

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