Vibration analysis of post-buckled fluid-conveying functionally graded pipe

The vibration of post-buckled fluid-conveying pipe made of functionally graded material is analyzed. The pipe material properties are assumed to be graded in the thickness direction according to power-law distribution. An exact solution is obtained for the post-buckling deformation of the fluid-conveying functionally graded pipe with various boundary conditions. The linear vibration problem is solved around the first buckled configuration and the natural frequencies of the three lowest vibration modes are obtained. The influences of power-law exponent, initial tension, fluid density and fluid velocity on the static deflection and free vibration frequencies are studied.