An innovative implementation of the skin concept for the reduction of the radiated sound power from a vibrating structure is proposed. The skin has a periodic structure and continuously covers a vibrating beam. Thus, this skin decouples the vibrating structure from the acoustic field by modifying the wavenumber spectrum of the radiating surface. First, structural acoustics and periodic structure theories are reviewed in order to predict how bending waves propagate along a periodic beam and how this beam radiates sound. These theories are then extended to the case of multi-layered structures in order to understand the behavior of a beam loaded with a periodic skin. In order to design the beam and skin structural periods, two different methods are used: Galois sequences and an optimization process using a real-valued genetic algorithm. Simulations are run for the case of periodic beams and beams coupled with periodic smart skins in both finite and infinite configurations. Results show that periodic beam can radiate less sound than equivalent uniform structures. Results also show the potential of periodic skin for application to the structural radiation problem for frequencies higher than approximately 100Hz with an approximately 10dB of radiated sound power attenuation.