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mathematics, beam, modelling

Authors :
Boutahar, Youssef
Lebaal, Nadhir
Bassir, David
Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB)
Université de Technologie de Belfort-Montbeliard (UTBM)-Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
IRAMAT - Laboratoire Métallurgies et Cultures (IRAMAT - LMC)
Institut de Recherches sur les Archéomatériaux (IRAMAT)
Université de Technologie de Belfort-Montbeliard (UTBM)-Université d'Orléans (UO)-Université Bordeaux Montaigne-Centre National de la Recherche Scientifique (CNRS)-Université de Technologie de Belfort-Montbeliard (UTBM)-Université d'Orléans (UO)-Université Bordeaux Montaigne-Centre National de la Recherche Scientifique (CNRS)
CB - Centre Borelli - UMR 9010 (CB)
Service de Santé des Armées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université Paris Cité (UPCité)
BASSIR, DAVID
Source :
Mathematics, Mathematics, 2021, 9 (12), pp.1422. ⟨10.3390/math9121422⟩
Publication Year :
2021
Publisher :
HAL CCSD, 2021.

Abstract

International audience; A refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams.

Details

Language :
English
ISSN :
22277390
Database :
OpenAIRE
Journal :
Mathematics, Mathematics, 2021, 9 (12), pp.1422. ⟨10.3390/math9121422⟩
Accession number :
edsair.od......1398..2a05e1b8140547846678ac2fd80c2c43
Full Text :
https://doi.org/10.3390/math9121422⟩