Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory

Belqassim Ayache, Riadh Bennai, Bouazza Fahsi, Hocine Fourn, Hassen Ait Atmane and Abdelouahed Tounsi

Abstract

A free vibration analysis and wave propagation of functionally graded porous beams has been presented in this work using a high order hyperbolic shear deformation theory. Unlike other conventional shear deformation theories, a new displacement field that introduces indeterminate integral variables has been used to minimize the number of unknowns. The constituent materials of the beam are assumed gradually variable along the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The variation of the pores in the direction of the thickness influences the mechanical properties. It is therefore necessary to predict the effect of porosity on vibratory behavior and wave velocity of FG beams in this study. A new function of the porosity factor has been developed. Hamilton\'s principle is used for the development of wave propagation equations in the functionally graded beam. The analytical dispersion relationship of the FG beam is obtained by solving an eigenvalue problem. Illustrative numerical examples are given to show the effects of volume fraction distributions, beam height, wave number, and porosity on free vibration and wave propagation in a functionally graded beam.

Key Words

higher-order beam theory; functionally graded beam; free vibration; wave propagation; porosity

Address

Belqassim Ayache: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Riadh Bennai: Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria Bouazza Fahsi: Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria Hocine Fourn: Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Hassiba Benbouali of Chlef, Algeria Hassen Ait Atmane: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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