Analysis of free vibration in bi-directional power law-based FG beams employing RSD theory

Nafissa Zouatnia , Lazreg Hadji , Hassen Ait Atmane , Mokhtar Nebab , Royal Madan , Riadh Bennai , Mouloud Dahmane

Abstract

The present study aims to investigate the free vibration of bi-directional functionally graded (BDFG) beams using a refined shear deformation (RSD) theory. Power law variation of material composition was considered along thickness and longitudinal directions. The beams are considered simply supported. The methodology adopted is the Hamilton principle and the governing equation was solved using Navier's method for simply supported boundary conditions. A metal-ceramic combination of materials was used to provide gradation as per power law variation. The equivalent elasticity modulus and density of BDFG were computed using the rule of mixture. The results of the study were related to published works and found to be a good match. The effect of grading parameters in the thickness and longitudinal direction was studied to investigate its impact on the natural frequency.

Key Words

BDFG beams; free vibration; Hamilton principle; refined shear deformation theory

Address

Nafissa Zouatnia — Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret, 14000, Algeria
Lazreg Hadji — Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret, 14000, Algeria; Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria
Hassen Ait Atmane — Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria
Mokhtar Nebab — Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria; Department of Civil Engineering, Faculty of Technology, University of M'Hamed BOUGARA Boumerdes, Algeria
Royal Madan — Department of Mechanical Engineering, Graphic Era (Deemed to be University), Dehradun 248002, Uttarakhand, India
Riadh Bennai — Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria
Mouloud Dahmane — Ecole National Superieur D'hydraulique, Blida, 09000, Blida, Algeria

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