NURBS-based vibration analysis of variable-stiffness free-form curved beams

Advanced AFP technologies have enabled the fabrication of variable angle tow composites, offering enhanced flexibility in stiffness tailoring for designing lightweight structures with superior vibration performance. This work investigates the free vibration of generally laminated curved beams featuring variable curvature and variable stiffness using an isogeometric analysis framework. The theoretical model is based on the Timoshenko deep beam theory, fully accounting for axial extensibility, shear deformation, and rotary inertia. Material coupling is approximately characterized via an equivalent modulus approach. The governing equations for free vibration are derived in weak form using Hamilton’s principle, and subsequently, an isogeometric formulation employing Non-Uniform Rational B-Splines (NURBS) is utilized to predict natural frequencies and corresponding mode shapes. A key novelty of this work is the establishment of a versatile framework applicable to more general curved beams, accommodating both free-form geometries and variable-stiffness layups. The accuracy and effectiveness of the proposed framework are validated against published benchmark results. Furthermore, the influences of fiber angle, material parameters, boundary conditions, and geometric configurations on the vibration characteristics of variable-stiffness free-form curved beams are examined in detail.