Nonlinear dynamics of PFG cylindrical shells reinforced with oblique stiffeners under viscous fluid flow

In this paper, the nonlinear dynamic (ND) behavior of porous functionally graded (PFG) cylindrical shells (CSs) reinforced with oblique stiffeners under viscous, compressible, and non‑isentropic internal fluid flow is comprehensively analyzed using a semi‑analytical approach. Moreover, this study investigates two variations of PFG: one featuring an even porosity distribution (EPD) and the other exhibiting an uneven porosity distribution (UEPD). Lekhnitskii’s smeared stiffener approach is utilized to model the stiffeners. The nonlinear governing equations (NGEs) are formulated based on Donnel shell theory (DST) incorporating von Kármán geometric nonlinearity. Then, these equations are discretized via Galerkin’s method, and a three-term approximate solution for the deflection is established. An approach utilizing the P-T method is developed for analyzing the ND behavior of PFG-CSs reinforced with oblique stiffeners in the presence of fluid flow, providing a continuous semi-analytical solution across the full-time domain with highly accurate numerical results. This method combines a piecewise-constant argument with Taylor series expansions, hence its designation as the P-T method. The study advances the state of the art by integrating oblique stiffener effects, porosity variations, and realistic fluid–structure interaction in the analysis of PFG-CSs, thereby capturing the influence of both material distribution and internal fluid properties on their ND responses. The results demonstrate that stiffener angles, porosity distribution, and fluid characteristics significantly affect the ND behavior, providing valuable insights and design guidelines for marine risers, heavy‑oil pipelines, and aerospace propellant tanks where fluid–structure interactions are critical to structural safety and performance.