Nonlinear Vibrations of Cracked GPLRC Variable-Thickness Cylindrical Curved Plates

Cylindrical curved plate structures act as essential components in critical applications including fuselages, cabin walls, and engine blades. They are extensively used in environments with complex loads and high temperatures. Studying their dynamic properties is crucial for guaranteeing engineering safety. This study definitively investigates the nonlinear vibration and chaotic dynamic behaviour of cracked GPLRC variable-thickness cylindrical plates. To ascertain the physical parameters of cracked GPLRC cylindrical curved plates with variable thickness, we utilized an enhanced Halpin–Tsai model and hybrid rules, considering four graphene sheet (GPL) distribution patterns and three pore structures in porous aluminum. We applied first-order shear deformation theory (FSDT) and von-Karman geometric nonlinearity model, using Hamilton principle, to derive the governing equations. The Williams crack tip progressive solution was innovatively introduced to rectify the displacement field, thereby establishing a dynamic framework for cracked curved plates. Consequently, the motion equations for cracked GPLRC variable-thickness cylindrical curved plates were derived. The system's nonlinear ordinary differential equations (ODEs) were obtained using Galerkin method for cantilever and simply supported boundary conditions. Runge-Kutta method was utilised to obtain numerical solutions, and a comprehensive set of bifurcation, phase, time history and three-dimensional phase diagrams were presented for cracked GPLRC variable-thickness cylindrical plates. We conducted a systematic analysis to examine how crack length, angle, and position quantitatively affect nonlinear responses.