Topological design of soft substrate acoustic metamaterial for mechanical tuning of sound propagation

The design of tunable acoustic waves is crucial in phononic crystals (PnCs), as acoustic waves exhibit continuous variation across diverse frequency ranges in practical applications. While there have been research efforts on tunable PnCs, existing design strategies predominantly rely on predetermined topology and scatterer shapes based on empirical experience. This reliance poses challenges in ensuring customized and reversible tuning of the bandgap. In this work, we present a customized tunable PnC design model and solution strategy based on soft substrates, which enables reversible tuning of a specific frequency/order bandgap. The designed structure consists of a soft substrate and crystalline columns dispersed in the soft substrate and air. The relative positions of the scatterers in the air are changed by stretching the substrate, thereby realizing the modulation of sound propagation. Since soft materials have both material nonlinearities and complex geometrical variations that are difficult to obtain design sensitivity information, the material-field series expansion topology optimization approach is employed to achieve custom tunable design of the bandgap. The paper presents simulation-based analyses and experimental verification of the customized bandgap opening and closing. The results demonstrate a close alignment between theoretical predictions of propagation curves and experimental findings. This concurrence serves as evidence that the soft-substrate PnC, derived through topology optimization, effectively facilitates the adjustment of bandgaps of arbitrary orders and enables switching between various acoustic functions.