The effect of various boundary conditions on the nonlinear dynamics of slightly curved pipes under thermal loading

Slightly curved pipes are prevalent in many industries including oil installations especially in the Delta regions of the world. The aim of this paper therefore is to investigate the nonlinear dynamics of these pipes conveying fluids under the influence of thermal loadings. These investigations are for three different boundary conditions, namely simply supported ends, clamped-clamped ends and clamped-simply supported ends respectively. To derive the governing equations, small strains of initial curvature, temperature, tension, pressure, longitudinal and transverse strains are considered. Furthermore, strains due to curvature change during bending which are hitherto neglected in most of the previous works on slightly curved pipes are added. The strain due to initial curvature accounts for the geometric imperfection. Two coupled nonlinear differential equations in both longitudinal and transverse directions are obtained and solved using eigenfunction expansion method, up to four modes. Linear natural frequencies were obtained, and is shown that for various boundary conditions, it increases as the initial curvature increases and decreases as thermal loading increases. The nonlinear results obtained show that the amplitude of the pipe motion becomes larger due to the obvious effect of thermal loading. Nonlinear results for both vanishing and non-vanishing longitudinal displacements are presented.