SUMMARY

Since the 17th century, the evolution of elastic wave manipulation has spanned centuries. In parallel, the realm of piezoelectric shunt damping currently faces a revolutionary phase driven by the emergence of synthetic impedance circuits, which holds the potential for digital programmability. Inspired by these developments, this thesis offers an experimental framework for the realization of two wave phenomena in elastic media: space-time wave localization and exceptional points (EPs). First, the concept of space-time wave localization using programmable defects is experimentally demonstrated. The dynamic properties of the local resonators of an electromechanical metamaterial, comprising piezoelectric elements connected to synthetic impedance circuits, are digitally controlled to modulate a trivial point defect in space and time. The experimental results show that the vibration energy is gradually transferred and localized over subsequent unit cells according to the defect position. In another topic, this thesis introduces an experimentally validated framework for creating tunable exceptional points in electromechanical waveguides. EPs are non-Hermitian singularities typically found in parity-time (PT) symmetric systems with balanced gain and loss. Here, piezoelectric transducers are shunted through synthetic impedance circuits that emulate resistors (responsible for the gain and loss) and inductors (responsible for the tunability), and whose properties can be programmed via software. While the inherent structural damping of the waveguide has the effect of breaking PT symmetry, we show that EPs can still be created by using non-trivial gain and loss combinations. Ultimately, the results in this thesis pave the way for the practical realization of space-time wave localization and EPs in elastic media, opening avenues for their application in information transmission, multiplexing and demultiplexing, enhanced sensing, and asymmetric wave control, for example.