Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties

Ammar Melaibari, Ahmed Amine Daikh, Muhammad Basha, Ahmed W. Abdalla, Ramzi Othman, Khalid H. Almitani, Mostafa A. Hamed, Alaa Abdelrahman and Mohamed A. Eltaher
Additional contact information
Ammar Melaibari: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Ahmed Amine Daikh: Department of Technology, University Centre of Naama, Naama 45000, Algeria
Muhammad Basha: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Ahmed W. Abdalla: Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig 44519, Egypt
Ramzi Othman: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Khalid H. Almitani: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Mostafa A. Hamed: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Alaa Abdelrahman: Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig 44519, Egypt
Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-24

Abstract: This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in the analysis. By employing Hamilton’s variational principle, the equations of motion are derived based on hyperbolic sine function shear deformation theory. Then, the derived equations are solved analytically using the Galerkin approach. Two types of material distribution are proposed. Higher-order nonlocal strain gradient theory is employed to capture influences of shear deformation, length scale parameter (nonlocal) and material/microstructurescale parameter (gradient). Temperature-dependent material properties are considered. The validation of the proposed mathematical model is presented. Detailed parametric analyses are carried out to highlight the effects of the carbon nanotubes (CNT) distribution pattern, the thickness stretching, the geometry of the plate/shell, the boundary conditions, the total number of layers, the length scale and the material scale parameters, on the vibrational frequencies of CNTRC laminated nanoplates and nanoshells.

Keywords: free vibration; nanoplates and nanoshells; CNTs; higher-order shear deformation theory; Galerkin method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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