Static and dynamic characteristics of the post-buckling of fluid-conveying porous functionally graded pipes with geometric imperfections

Abstract

Abstract In this study, the static and dynamic responses of functionally graded material (FGM) pipes with porosities and geometric imperfections are investigated. The material properties of the porous FGM pipe are assumed to vary continuously and smoothly along the radial direction based on the modified power-law distribution. The nonlinear equations of motion are derived on the basis of the Euler-Bernoulli beam hypothesis incorporating the effects of von Karman nonlinearity and initial imperfection. Two general cases of pipes with movable and immovable ends are considered. Closed-form solutions for nonlinear critical buckling velocity and nonlinear stability behavior of system under different boundary conditions are proposed. Subsequently, the free vibration problem around the buckled configuration is solved as a eigenvalue problem, and the natural frequencies are calculated using a new exact solution procedure that considers the gyroscopic effect. The effects of important parameters including the initial imperfection, the power-law index, the porosity volume fraction, and geometric properties on buckling and post-buckling behavior of system are explored in numerical results.