Rib-enforced thin shells have wide application in aircraft fuselages, offshore photovoltaic membranes as well as ship and submarine hulls by virtue of a convenient stiffness-to-weight ratio combined with improved buckling characteristics. Central to the design of these structures is the vibrational reduction performance aimed at averting the onset of undesired resonance phenomena while controlling the noise operational profile. Within a compacted design-to-analysis framework empowered by the higher-continuity NURBS-based simulation capabilities offered by the on-trend isogeometric analysis (IGA) paradigm, we explore the relevance of selecting a suitable topology of the stiffener net protruding over the skin of a thin shell, having a predefined planar footprint, with respect to the modal behavior of the overall structure. In the setting of the open-source IGA library G+Smo [1], use is made of the emerging embedding concept [2] according to which slender enhancements are directly modelled as univariate curves embedded inside the bivariate parameterization of the underlying thin-walled manifold. As a result of the inherently strong rib-shell coupling, the computational frame benefits from the absence of auxiliary compatibility relations. Further, tedious global re-meshing techniques can be avoided owing to the independence of the discretization of the local entities. Numerical examples highlight the modal characteristics of ribbed shells, whose stiffeners obey the kinematics of geometrically nonlinear warping-free Euler beams. The contribution is substantiated with a preliminary validation phase, where the isogeometric prediction is assessed against the solution of a commercial finite element code.