On frequency response of FG-CNT reinforced composite pipes in thermally pre/post buckled configurations

Abstract

This paper presents a theoretical analysis for the frequency response of thermally pre/post buckled composite pipes reinforced with carbon nanotubes (CNTs). The vibrational behavior of the uniformly heated nanocomposite pipe surrounded by a nonlinear elastic foundation is analytically studied. The nanocomposite media is introduced using a refined rule of mixtures that is calibrated with the available data on the basis of molecular dynamics simulations. Distribution of CNTs across the radius of composite pipes can be uniform or functionally graded (FG) and properties are considered to be temperature-dependent. A higher-order shear deformation model and the von Kármán assumption are employed to extract the nonlinear equations of motion. The system of partial differential equations is established by means of Hamilton’s principle. A two-step perturbation method is utilized to carry out closed-form solutions for these nonlinear equations. The natural frequencies are obtained for the immovable simply-supported boundary conditions. A comparison study is provided for the case of isotropic homogeneous pipes in which good agreement is obtained. The novel numerical results are presented to show the influences of geometric characteristics, CNT distribution pattern, foundation stiffness, and the CNT volume fraction upon the frequency response of the nanocomposite pipe subjected to uniform temperature rise loading.