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Structural Engineering and Mechanics
  Volume 81, Number 4, February25 2022 , pages 461-479

Vibration analysis of FG reinforced porous nanobeams using two variables trigonometric shear deformation theory
Abderraouf Messai, Lahcene Fortas, Tarek Merzouki and Mohammed Sid Ahmed Houari

    A finite element method analysis framework is introduced for the free vibration analyses of functionally graded porous beam structures by employing two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element. A comprehensive parametric study is carried out, with a particular focus on the effects of various structural parameters such as the dispersion patterns of GPL reinforcements and porosity, thickness ratio, boundary conditions, nonlocal scale parameter and strain gradient parameters. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams.
Key Words
    finite element method; free vibration; functionally graded porous materials; nonlocal strain gradient theory; variational formulation
Abderraouf Messai: Department of Civil Engineering, University Ferhat Abbas SETIF 1, SETIF, Algeria
Lahcene Fortas: MN2I2S Laboratory, Faculty of Science and Technology, Biskra University, Biskra, Algeria
Tarek Merzouki: LISV, University of Versailles Saint-Quentin, 10-12 Avenue de l'Europe, 78140 Vélizy, France
Mohammed Sid Ahmed Houari: Laboratoire d

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