This paper proposes a new tool for the selection of optimal elementary shunts connected to piezoelectric patches, which are bonded on thin structures to control the multi-resonant flexural vibration produced by broadband stochastic excitations. More specifically, the study introduces a procedure for the identification of simple shunt architectures composed by a small-number of low-value RLC elements, which yet produce significant multi-resonant vibration control effects. The challenge to identify beneficial elementary shunts lies in the fact that numerous candidate circuits exist, and this number grows exponentially with the increase of allowed electrical components. To this end, a design optimisation procedure is proposed, which enables the characterisation of all candidate shunt networks with a pre-defined number of elements having a given range of values. The paper refers to a practical model-problem, which encompasses a thin plate equipped with five piezoelectric patches connected to shunts. A trial design study is illustrated, where the tool is used to find suitable simple shunts to control the resonant responses of 6 flexural modes of the plate in a frequency band comprised between 20 and 150 Hz. The full set of shunt circuits composed by 4 elements is systematically searched and two simple shunts are identified. The physics and control performance of these two shunts are contrasted with those of classical single-resonant and multi-resonant shunts. The study shows that these elementary shunts generate 6 to 16 dB reductions of the target resonant responses, which are comparable to those that would be produced by a classical six-branches multi-resonant shunt encompassing 18 elements. Moreover, it shows that the two shunts produce combined absorption and damping effects such that they can provide beneficial vibration control in presence of significant variations of the flexural response of the structure too.
