On the Stability of Spinning Functionally Graded Cantilevered Pipes Subjected to Fluid-Thermomechanical Loading

This paper studies the thermomechanical stability of a cantilevered pipe spinning along its longitudinal axis and carrying an internal axial flow. The pipe, made of functionally graded materials (FGMs), is subjected to an axial force at the free end operating in a high temperature environment. It is modeled by the Rayleigh beam theory and is considered as a hollow thin-walled beam. The equation of motion, along with the boundary conditions, for the pipe is derived by using the extended Hamilton's principle. Further, the extended Galerkin's method (EGM) in conjunction with a proper representation of the displacements of the pipe is used to solve the eigenvalue problem. Depending upon the nature of the eigenvalues, i.e. real or complex-conjugate, the conditions for occurrence of instability by flutter or by divergence are derived. The effects of spin rate and velocity of fluid flow are studied on the stability regions, i.e. the critical flutter and divergence boundary, by the numerical method. Also, the effects of parameters, such as fluid mass ratio, compressive axial force, volume fraction index of the FGM and temperature gradient through the pipe thickness, are considered in developing the stability map for the spinning cantilever pipe. The results are compared with those available in the literature and good agreement has been achieved.