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Wave propagation in mechanical structures can be controlled by a coupling to an electrical network exhibiting a similar dispersion relation. The energy transfer between the two media is maximized on a broad frequency range when choosing a network that is the electrical analogue of the structure to control. In terms of structural vibration, this strategy is equivalent to a multimodal tuned mass damping. Indeed, the control is implemented thanks to a multimodal electrical network, whose modes are close enough to those of the mechanical structure. The electromechanical coupling can be achieved by using an array of piezoelectric patches, which are small enough compared to the smallest wavelength to control. Then, when considering interconnected patches, wave propagation occurs simultaneously in the mechanical and electrical media. Wave propagation in one-dimensional periodic structures can be analyzed with the transfer matrix method. In this paper, the definition of an electromechanical unit cell gives a relation between state vectors involving both mechanical and electrical degrees of freedom. As an extension of a previous work focusing on longitudinal propagation, four transfer matrix models are defined in order to describe the piezoelectric coupling of a beam to its discrete electrical analogue. Indeed, the beam can be approximated either by its discrete equivalent, a fully homogenized model, a piecewise homogenized model or a finite element model. Offering an increasing complexity, those formulations are compared in order to determine their respective limits. Depending on the frequency range of interest, it then becomes possible to choose a suitable model for the analysis of structures involving a piezoelectric coupling to their electrical analogues.

TRANSVERSE WAVE PROPAGATION IN A ONE-DIMENSIONAL STRUCTURE COUPLED TO ITS ELECTRICAL ANALOGUE: COMPARISON OF TRANSFER MATRIX MODELS