Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory

Abderrahmane Mouffoki , E.A. Adda Bedia , Mohammed Sid Ahmed Houari , Abdelouahed Tounsi , S.R. Mahmoud

Abstract

In this work, the effects of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is studied by proposing a novel simple trigonometric shear deformation theory. The main advantage of this theory is that, in addition to including the shear deformation influence, the displacement field is modeled with only 2 unknowns as the case of the classical beam theory (CBT) and which is even less than the Timoshenko beam theory (TBT). Three types of environmental condition namely uniform, linear, and sinusoidal hygrothermal loading are studied. Material properties of FG beams are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from Hamilton

Key Words

free vibration; trigonometric shear deformation beam theory; functionally graded nanobeam; nonlocal elasticity theory; hygrothermal effect

Address

Abderrahmane Mouffoki — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
E.A. Adda Bedia — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Mohammed Sid Ahmed Houari — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Université Mustapha Stambouli de Mascara, Department of Civil Engineering, Mascara, Algeria
Abdelouahed Tounsi — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia; Mathematics Department, Faculty of Science, University of Sohag, Egypt

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