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

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