Mahmood Heshmati

Significant developments in manufacturing process provide the possibility of producing functionally graded materials (FGMs) with two and three dimensional gradients using computer aided fabrication processes. Two directional functionally graded materials (2D-FGMs) are usually fabricated by continuous combination of three or four different material phases such ceramics and metal alloys. In this paper, vibration and stability of a new pipe made of two directional functionally graded materials (2D-FGMs) is studied. The inner surface of the pipe is assumed to be made of two distinct ceramics and the outer surface of two metals. The continuously variation for volume fractions of the constituent materials through the radial and axial directions is considered based on a power law material distribution. The governing differential equations of the problem are derived based on the Euler-Bernoulli beam theory. The finite element method is employed to discretize the equations of motions. Finally, a modal analysis is adopted to calculate the critical flow velocities of a pipe with clamped-clamped end conditions. Different power law exponents have been investigated. The present results show that using 2D-FG pipe leads to a more flexible design than conventional 1D-FG pipe.