Nonlinear thermo-resonant behavior of fluid-conveying FG pipes

Document Type


Publication Date



Department of Mechanical Engineering-Engineering Mechanics


In the current paper, an attempt is made to analyze the moderately large oscillations of a geometrically nonlinear functionally graded pipe conveying hot fluid subjected to a harmonic lateral excitation. The material properties of functionally graded pipe are presumed to vary continuously and smoothly through its radial direction according to a power law function. In addition, the temperature-dependency of material properties for both the pipe and fluid are taken into account. The equations of motion of the system in the form of partial differential equations (PDEs) are derived by implementing the Euler-Bernoulli beam hypothesis and the von-Karman geometric nonlinearity. The achieved PDEs are discretized to a set of nonlinearly coupled ordinary differential equations via the Galerkin technique. In order to assess the nonlinear thermo-resonant characteristics of the system, the method of harmonic balance is employed. Furthermore, the temperature distribution in the radial direction of pipe is calculated by use of the one-dimensional steady stead heat conduction model in conjunction with the Galerkin technique. The nonlinear thermo-resonant behavior of the system accompanied by bifurcations is examined via constructing the frequency-amplitude, force-amplitude, and backbone curves. In addition, the role of gyroscopic damping in the nonlinear resonant responses of system is explored. Eventually, the comparative studies for a homogeneous isotropic pipe conveying fluid in the reference temperature are conducted by employing numerical results available in the scientific literature.

Publisher's Statement

© 2019 Elsevier Ltd. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.ijengsci.2019.103141

Publication Title

International Journal of Engineering Science