Investigating parametric homogenization models for natural frequency of FGM nano beams

Abdelhak Berkia; Billel Rebai; Bilal Litouche; Soufiane Abbas; Khelifa Mansouri; Abdelhak Berkia; Billel Rebai; Bilal Litouche; Soufiane Abbas; Khelifa Mansouri

doi:10.3934/matersci.2023048

AIMS Materials Science

2023, Volume 10, Issue 5: 891-908. doi: 10.3934/matersci.2023048

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Research article

Investigating parametric homogenization models for natural frequency of FGM nano beams

1.
Faculty of Sciences & Technology, Mechanical Eng Department, University Abbes Laghrour Khenchela, Algeria
2.
Faculty of Sciences & Technology, Civil Eng Department, University Abbes Laghrour Khenchela, Algeria
3.
Mechanic and Electro-Mechanic Department, University Center Abdelhafid Boussouf, Mila, Algeria
4.
LMRS Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Algeria
5.
Laboratory of Eng and Sciences of Advanced Materials (ISMA), Khenchela, Algeria

Received: 24 July 2023 Revised: 11 September 2023 Accepted: 19 September 2023 Published: 12 October 2023

This research focuses on exploring the free vibration behavior of functionally graded (FG) nano-beams. To calculate the effective properties of the FG nano-beam, which varies solely in the thickness direction, the four homogenization schemes Mori-Tanaka, Tamura, Reuss and Voigt are employed. This study employs high-order shear deformation nano-beam theory and derives the governing equations of motion using nonlocal differential constitutive relations of Eringen. Hamilton's principle is utilized in conjunction with the refined three variables beam theory. The consideration of a length scale parameter accounts for small-scale effects. Analytical solutions are obtained for a simply supported FG nano-beam and compared with existing literature solutions. The research also investigates the influence of different homogenization schemes, the nonlocal parameter, beam aspect ratio and various material compositions on the dynamic response of the FG nano-beam.
- Hamilton's principle,
- length scale parameter,
- Eringen theory,
- free vibration,
- homogenization models,
- nano-beams
Citation: Abdelhak Berkia, Billel Rebai, Bilal Litouche, Soufiane Abbas, Khelifa Mansouri. Investigating parametric homogenization models for natural frequency of FGM nano beams[J]. AIMS Materials Science, 2023, 10(5): 891-908. doi: 10.3934/matersci.2023048

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Abstract

This research focuses on exploring the free vibration behavior of functionally graded (FG) nano-beams. To calculate the effective properties of the FG nano-beam, which varies solely in the thickness direction, the four homogenization schemes Mori-Tanaka, Tamura, Reuss and Voigt are employed. This study employs high-order shear deformation nano-beam theory and derives the governing equations of motion using nonlocal differential constitutive relations of Eringen. Hamilton's principle is utilized in conjunction with the refined three variables beam theory. The consideration of a length scale parameter accounts for small-scale effects. Analytical solutions are obtained for a simply supported FG nano-beam and compared with existing literature solutions. The research also investigates the influence of different homogenization schemes, the nonlocal parameter, beam aspect ratio and various material compositions on the dynamic response of the FG nano-beam.

References

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