Analytical and numerical study of vibration and transient heat conduction in a functionally graded pipe

Abstract

Functionally graded material (FGM) is an advanced class of composite material. In FGM, the volume fraction of each constituent can be tailor-made across the thickness for desired applications. In this paper, the analytical solution and numerical simulation of free vibration and transient heat conduction problem in a functionally graded pipe are considered. 3D elasticity theory is adopted for considering the thickness effect in the natural frequency derivation. For solving the transient heat conduction problem in FG pipe, the extended shifting variable method is used. A multi layer model is considered to numerically simulate the vibration and transient heat conduction behavior of FG pipe using standard finite element method package. Results obtained from both analytical solution and numerical simulations are compared for the free vibration and transient heat conduction. The 8- and 16- layer models show the higher accuracy for simulating FG pipe. For 16-layer model, the difference in natural frequency between numerical results and analytical solution is under 0.18%. The transient temperature distribution at specific position of the FG pipe is obtained from transient heat conduction study for various FG power law indices. The free vibration and transient temperature distribution of the FG pipe will help to tailor the FG pipe by adjusting the graded ways for specific application.

Keywords

• functionally graded pipe
• free vibration
• elasticity
• transient heat conduction
• numerical simulation