In piezoelectric shunt damping, an array of patches can be a solution to control vibration over a broad frequency range. Implementing a multimodal electrical network gives the possibility to act on several mechanical modes simultaneously. For the study of one-dimensional structures, a periodic layout enables the use of a transfer matrix method that applies on electromechanical state-vectors. Various models can be used to describe the electromechanical unit cells. Indeed, even if the electrical medium is discrete, the mechanical structure can be approximated either by its discrete equivalent, by its homogenized forms or by its finite element model. Offering an increasing complexity, those formulations are compared in order to define their respective limits. It is especially focused on vibration reduction expectations when the considered wavelength is approaching the length of the piezoelectric patches. Depending on the frequency range of interest, it is then possible to choose a suitable model for the analysis of damping systems involving a piezoelectric network.