Nonlinear dynamic analysis of axially moving obliquely stiffened FG-CNTRC cylindrical shells under partially distributed loading

This paper explores the nonlinear vibration (NV) and nonlinear dynamic buckling (NDB) behavior of axially moving obliquely stiffened functionally graded (FG) carbon nanotube (CNT) reinforced composite cylindrical shells (CSs) exposed to an external dynamic excitation applied over a specified axial position and a defined loaded length. Both the shell and the oblique stiffeners (OSs) are made of FG-CNT material. Four CNT distribution schemes are examined within the shell: FG-Λ, FG-V, FG-X, and uniformly distributed (UD). A mechanical model is developed for FG-CNT composite CSs stiffened by two crossing families of OSs, allowing the stiffener orientations may be either identical or different. The contribution of the OSs is incorporated through smeared stiffener technique. The governing dynamic equations are formulated within the context of Donnell shell theory (DST) combined with von Kármán-type geometric nonlinear strain-displacement relations and then reduced to a system of coupled nonlinear ordinary differential equations using the Galerkin procedure. Accordingly, the NV and NDB responses investigated in this study are interpreted within a geometrically nonlinear reduced-order shell formulation, rather than a fully nonlinear large-deformation framework. To evaluate how the main parameters affect the NV and NDB behavior, the P-T method is employed. This approach yields a smooth and original semi-analytical solution throughout the full time interval under consideration and leads to more accurate and reliable numerical predictions. The study offers a detailed assessment of the system’s nonlinear response, highlighting the roles of various material and geometric parameters. The results can serve as useful benchmarks for researchers and engineers engaged in the design and evaluation of axially moving obliquely stiffened FG-CNT reinforced composite CSs.