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Steel and Composite Structures Volume 39, Number 1, April10 2021 , pages 95-107 DOI: https://doi.org/10.12989/scs.2021.39.1.095 |
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Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory |
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Redhwane Ait Atmane, Noureddine Mahmoudi, Riadh Bennai,
Hassen Ait Atmane and Abdelouahed Tounsi
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| Abstract | ||
| In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams. | ||
| Key Words | ||
| functionally graded beams; higher shear deformations theories; variable elastic foundations; porosity | ||
| Address | ||
| Redhwane Ait Atmane: Laboratoire Génie Industriel et Développement Durable, Faculty of Technology, University of Relizane, Algeria Noureddine Mahmoudi: Department of Mechanical Engineering, University of Saida, Algeria Riadh Bennai: Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria Hassen Ait Atmane: Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea | ||