Tuning collective actuation of active solids by optimizing activity localization†

Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then condensates on a small fraction of the vibrational modes, the selection of which obeys non trivial rules rooted in the nonlinear part of the dynamics. So far, the complexity of the selection mechanism has limited the design of specific actuation. Here, we investigate numerically how localizing activity to a fraction of modes enables the selection of non-trivial collective actuation. We perform numerical simulations of an agent-based model on triangular and disordered lattices and vary the concentration and the localization of the active agents on the lattice nodes. Both contribute to the distribution of the elastic energy across the modes. We then introduce an algorithm, which, for a given fraction of active nodes, evolves the localization of the activity in such a way that the energy distribution on a few targeted modes is maximized – or minimized. We illustrate on a specific targeted actuation, how the algorithm performs as compared to manually chosen localization of the activity. While, in the case of the ordered lattice, a well-educated guess performs better than the algorithm, and the latter outperform the manual trials in the case of the disordered lattice. Finally, the analysis of the results in the case of the ordered lattice leads us to introduce a design principle based on a measure of the susceptibility of the modes to be activated along certain activation paths.