Nonlinear transverse vibration of functionally graded cylindrical shell conveying fluid flow embedded in elastic medium

Geometrically nonlinear vibrations of functionally graded (FG) circular cylindrical shells, conveying incompressible flow subjected to thermal variations and embedded in an elastic medium are investigated via energy approach in this study. Using Lagrange equations of motion, the energy functional is reduced to a system differential equations. This system lose stability by divergence when the flow velocity reaches a critical value. The divergence is strongly subcritical, becoming supercritical for larger amplitudes. Therefore the shell, if perturbed from the initial configuration, has severe deformations causing failure much before the critical velocity predicted by the linear threshold. Donnell'snon-linear theory retaining in-plane displacements are used for the shell. The fluid is modeled by potential flow theory but the effect of steady viscous forces is taken into account. simply supported boundary conditions are used to simulate the conditions. The effects of FGM volume fraction exponent index, temperature variations, flow velocity, fluid Viscosity and elastic medium on the frequency–amplitude nonlinear response are discussed.