Open Access

ARTICLE

Bending and Free Vibration Analysis of Porous-Functionally-Graded (PFG) Beams Resting on Elastic Foundations

by Lazreg Hadji^1,2,*, Fabrice Bernard³, Nafissa Zouatnia⁴

1 Laboratory of Geomatics and Sustainable Development, University of Tiaret, Tiaret, 14000, Algeria
2 Department of Mechanical Engineering, University of Tiaret, Tiaret, 14000, Algeria
3 INSA Rennes, Laboratory of Civil Engineering and Mechanical Engineering, Rennes, 35043, France
4 Department of Civil Engineering, University of Tiaret, Tiaret, 14000, Algeria

* Corresponding Author: Lazreg Hadji. Email:

(This article belongs to the Special Issue: Materials and Energy an Updated Image for 2021)

Fluid Dynamics & Materials Processing 2023, 19(4), 1043-1054. https://doi.org/10.32604/fdmp.2022.022327

Received 04 March 2022; Accepted 29 March 2022; Issue published 02 November 2022

Abstract

The bending and free vibration of porous functionally graded (PFG) beams resting on elastic foundations are analyzed. The material features of the PFG beam are assumed to vary continuously through the thickness according to the volume fraction of components. The foundation medium is also considered to be linear, homogeneous, and isotropic, and modeled using the Winkler-Pasternak law. The hyperbolic shear deformation theory is applied for the kinematic relations, and the equations of motion are obtained using the Hamilton’s principle. An analytical solution is presented accordingly, assuming that the PFG beam is simply supported. Comparisons with the open literature are implemented to verify the validity of such a formulation. The effects of the elastic foundations, porosity volume percentage and span-to-depth ratio are finally discussed in detail.

---

Graphic Abstract

---

Keywords

---