Dynamic behaviour of fluid-transporting axially functionally graded non-uniform Rayleigh pipes lying on variable two-parameter elastic foundation

Abstract

The vibration characteristics of an axially functionally graded (AFG) non-uniform Rayleigh pipes transporting an inviscid fluid are investigated in this paper. The whole span of the pipe is assumed to rest on a variable elastic two-parameter foundation. It is also assumed that the moment of inertia, cross-sectional area, material density, modulus of elasticity of the pipe and the two moduli of the foundation are all functions of the coordinate along the axis of the pipe. Three types of distinct vibrating configurations namely, Pinned-Pinned, Clamped-Pinned and Clamped-Clamped end conditions are considered. The objectives are three-fold, viz: to (i) compute accurately the natural frequencies of the Rayleigh pipes under consideration (ii) the second determine and analyze the influence of rotatory inertia parameter, foundation stiffness parameters, non-uniform terms, material gradient index parameter, mass ratio and the fluid flow velocity on the natural frequencies of the vibrating pipe, thereby coming up with some conclusions concerning the dynamic behaviour of the pipe under consideration, and (iii) the third objective is to develop the variational iteration method (VIM) scheme for examining vibration characteristics of non-uniform AFG fluid-transporting Rayleigh pipe lying on variable Pasternak foundation. The pertinent analysis is carried out by solving the governing boundary-value problem via a semi-analytical technique known as variational iteration method (VIM). It is found that (i) for the purpose of validation the results obtained for the vibration frequencies of the pipe with no fluid flow which are compared with the results earlier reported in the literature yield good agreement (ii) the natural frequencies of the pipe system under consideration decrease with an increase in rotatory inertia parameter (iii) the natural frequencies of the vibrating pipe decrease with increasing mass ratio parameter, velocity of the fluid flow and the non-uniform parameter of the foundation, respectively (iv) an increase in the material non-homogeneity parameter leads to an increase in the natural frequencies of the AFG non-uniform fluid-transporting Rayleigh pipe lying on variable Pasternak foundation. Finally, the issue of convergence of the solution is also discussed.