Free vibration of functionally graded carbon nanotubes reinforced composite nanobeams

Miloud Ladmek , Abdelkader Belkacem , Ahmed Amine Daikh , Aicha Bessaim , Aman Garg , Mohammed Sid Ahmed Houari , Mohamed-Ouejdi Belarbi , Abdelhak Ouldyerou

Abstract

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

Key Words

higher order nonlocal strain gradient theory; nanobeams; Navier's solution; novel trigonometric FGM; vibration

Address

Miloud Ladmek — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P., Mascara 29000, Algeria
Abdelkader Belkacem — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P., Mascara 29000, Algeria
Ahmed Amine Daikh — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P., Mascara 29000, Algeria; Department of Technology, University Centre of Naama, Naama 45000, Algeria
Aicha Bessaim — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P., Mascara 29000, Algeria
Aman Garg — Department of Civil Engineering, National Institute of Technology, Kurukshetra, Haryana 136119, India; Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India
Mohammed Sid Ahmed Houari — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P., Mascara 29000, Algeria
Mohamed-Ouejdi Belarbi — Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria
Abdelhak Ouldyerou — Department of Engineering Management, College of Engineering, Prince Sultan University, Riyadh, 11586, Saudi Arabia; Department of Mechanical Engineering, Faculty of Science and Technology, University of Mascara, Mascara, Algeria

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