Free vibration analysis of nonlinearly dispersed FG-CNTRC beams on Kerr substrate using an improved FSDT

Qais Gawah, Mazen Anwar Abdullah, Mohammed A. Al-Osta, Fouad Bourada, Abdeldjebbar Tounsi, Abdelouahed Tounsi and Murat Yaylaci

Abstract

This work analyzes the free vibration responses of a functionally graded carbon-nanotube reinforced composite (FGCNTRC) beam supported by Kerr substrates. Four carbon-nanotube (CNT) dispersion patterns following nonlinear forms are considered in the analysis. In the proposed model, the transverse displacement accounts for shear and bending, and the shear strain incorporates a correction function to refine its distribution across the beam's thickness. The mixture rule implements the estimation of the effective material properties. The kinematics is based on an improved first-order shear deformation theory (FSDT) framework. Deriving the governing equations of motion was through the application of Hamilton's principle. The obtained results are compared with those found in the literature to verify the current theory and its accuracy. The parametric study examines the impact of Kerr foundation parameters, CNT's configuration, and volume fractions, and the exponent degree of nonlinearity on the vibration behaviors of an FG-CNTRC beam.

Key Words

carbon nanotubes; composite beams; first-order; functionally graded; Kerr substrate; vibration

Address

Qais Gawah, Mazen Anwar Abdullah: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Mohammed A. Al-Osta: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia Fouad Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Mechanical Engineering Department, Faculty of Science and Technology, University of Rélizane, Algeria Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdogan University, 53100, Rize, Turkey; Faculty of Turgut Kiran Maritime, Recep Tayyip Erdogan University, 53900, Rize, Turkey

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