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This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels. The stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT). The present method models the plate and the stiffener separately, which allows the stiffener element nodes to not coincide with the plate shell-element nodes. The stiffness and mass matrices of a stiffener are transformed to those of the plate through the displacement compatibility conditions at the plate/stiffener interface by interpolation using NURBS basis functions. Cutouts are modeled using a single NURBS patch generated by creating a ruled surface between two curves. The proposed formulation is first validated by comparing it with available literature. The effects of width-to-thickness ratio, fiber orientation, ply layups, shape and size of the cutouts and the boundary conditions on the response of stiffened composite plates are then analyzed and the numerical results are used to derive useful conclusions.