A Unified Framework for Free Vibration Analysis of Variable-Angle Tow Composite Shells with Spatially Varying Curvature

The combination of variable-angle tow composites with shell geometries presents significant potential in various engineering and technical applications, particularly with regard to structural performance. Nevertheless, the numerical modeling of these structures can be challenging, as the larger number of unknowns significantly increases computational effort. The Carrera’s unified formulation has demonstrated promising results in the analysis of plates and shells reinforced with curvilinear fibers, offering an effective balance between numerical accuracy and the number of variables. This paper extends the unified formulation to more complex variable-angle tow shell structures characterized by variable curvature radii within their physical domain. The governing equations of the dynamic problem are derived using a displacement-based variational method, and the results are validated through comparisons with reference solutions from Abaqus 3D models. The First-Order Shear Deformation Theory (FSDT) is presented for a broader comparison of the proposed models. The maximum percentage error in terms of frequency shift observed for the FSDT model is 3.44%, whereas the corresponding error for the most refined model is only 0.19%. Across all examined cases, the computed fundamental frequencies and mode shapes closely match the reference results, demonstrating the reliability and effectiveness of the proposed method.