Stiffened structures are very common in engineering applications, for instance the wing of an airplane or the pressure hull of a submarine; both are subject to an excitation due to their movement in the fluid around, namely the Turbulent Boundary Layer (TBL) excitation. For improving the knowledge about the interaction between stiffened structures and TBL, this paper deals with the modelling of infinite periodically rib-stiffened plates excited by TBL. The mathematical formulation of the problem is well established in the literature. The originality of the present work relies on the use of a reciprocity technique for evaluating the response of the plate to convected harmonic pressure waves. The present approach allows then to compute the vibro-acoustic response of the plate due to the TBL from the response of the stiffened plate to a point mechanical force and to an acoustic monopole. Results in the physical space and the wavenumber space show the filter effect of the stiffened plate and the role of the supersonic domain on the far field radiation. They allow us to interpret the influence of the periodicity of the stiffeners on the vibration and the far-field noise for plates excited by TBL.