Nonreciprocal wave transmission: (a) Schematic of a beam structure with a spatiotemporally modulated section in the middle. The spatiotemporal modulation results in a nonreciprocal wave propagation allowing wave to propagate from right to left and blocking waves from left to right. (b) The stiffness modulation diagram for the structure is shown in space and time.

We introduce the first experimental demonstration of a broadband mechanical beam waveguide, which can be reconfigured to represent wave nonreciprocity. This is achieved by using spatiotemporal stiffness modulation with piezoelectric patches in a closed-loop controller. Using a combination of analytical methods, numerical simulations, and experimental measurements, we show that contrary to the conventional shunted piezoelectrics or nonlinearity based methods, our setup is stable, less complicated, reconfigurable, and precise over a broad range of frequencies. Our reconfigurable nonreciprocal system has potential applications in phononic logic, wave diodes, energy trapping, and localization.

In this project we:

• Proposed and designed a feedback/forward controller to spatiotemporal modulate the metamaterial’s stiffness using MATLAB
• Configured and analyzed wave propagation in the controlled system with 15% variable stiffness using MATLAB/COMSOL
• Studied and validated wave propagation experimentally using piezo sensors/actuators, hardware-in-the-loop, Simulink & dSPACE
• Analyzed the real-time data and investigated the nonreciprocity feature of the controlled system using MATLAB/Simulink

Band diagrams of an aluminium beam (a) Complete bandgap for only space modulated beam. (b) Directional and complete bandgaps in the beam with (c) Directional bandgaps in the beam (d) Wavenumber bandgap.

(a) The schematic of the spatiotemporally modulated beam with PZT actuators (blue) and sensors (red) bonded on both sides of the beam. (b) The stiffness modulation coefficient of three consecutive PZT patches over time. Note that the phase difference between consequent patches results in spatial modulation. (c) The schematic of the closed-loop feedback controller to implement the active modulation. (d) The numerical transfer function (ratio between transmitted wave to incident wave) without any modulation (black-line) and with spatial modulation for waves propagating left-to-right (red line) and waves propagating right-to-left (blue line). Since there is no time modulation, the results are identical for both LR and RL propagations. The yellow boxes indicate the bandgaps. (e) Numerically calculated transmission ratio for the spatiotemporally modulated beam for waves propagating RL (blue line) and LR (red line). The red boxes indicate the nonreciprocal bandgaps.

(a) Schematic of the experimental setup showing the beam, absorbing patches, PZTs sensors and actuators, piezodrives, MFC actuators, controller, and the laser. MFCs on both sides are used to introduce the wave to the system. The wave amplitude is measured before/after the first/last PZTs using a laser vibrometer. (b) Experimental setup. (c) The experimental measurements of transmission ratio without any modulation (solid black line) and with spatial modulation for wave propagating LR (red) and RL (blue). Note that the transmission ratio for RL and LR wave are identical. The bandgaps are indicated with the yellow box. (d) Transmission ratio in presence of spatiotemporal modulation for LR (red) and RL (blue) waves. The nonreciprocal bandgaps are identified with the red box.