In damping devices involving piezoelectric elements, charge cancelation or vibration node locations induce that a singlepiezoelectric patch cannot consistently achieve a multimodal control. In order to sense and control vibration on a prescribed frequency range, a solution consists in using an array of several piezoelectric patches being small compared to the smallest wavelength to control. Then, as an extension of the tuned mass damper strategy, a passive multimodal control requires to implement a damping system whose modes are as close as possible to those of the controlled structure. In this way, the electrical equivalent of the discretized mechanical structure represents the passive network that optimizes the energy transfer between the two media. For one-dimensional structures, a periodic distribution in several unit cells enables the use of the transfer matrix method applied on electromechanical state-vectors. The optimal passive networks are obtained for the propagation of longitudinal and transverse waves and a numerical implementation of the coupled behavior is performed. Compared to the more classical resonant shunts, the network topology induces promising multimodal damping and a reduction of the needed inductances. It is thus possible to create a completely passive electrical structure as it is demonstrated experimentally by using only purely passive components.