Free Vibration Analysis of Carbon-Nanotube-Reinforced Beams Resting on a Viscoelastic Pasternak Foundation by the Nonlocal Eshelby–Mori–Tanaka Method

Abstract

The scale effect of carbon nanotubes (CNTs) in the macro CNT-reinforced composites (CNTRCs) is analyzed, and the free vibration characteristics of a CNT-reinforced composite beam resting on a viscoelastic foundation were studied. By combining the nonlocal theory with the Eshelby–Mori–Tanaka (EMT) method, a nonlocal EMT constitutive equation considering the scale effect of CNTs in the macro CNTRCs is proposed. Based on the constitutive equation and the Timoshenko beam theory, the governing equations and corresponding boundary conditions of the CNT-reinforced composite beam resting on a viscoelastic Pasternak foundation are obtained by using the Hamilton principle. Then, a solution of free vibrations of the composite beam under simply supported boundary conditions is found. A comparative analysis of the results obtained in this study and in the previous literature verified the reliability of the model built and the solution method used.