<p>Creating tunable and linear elastic systems that enable broadband nonreciprocal elastic wave propagation may provide versatile control over mechanical signals within various ultrasonic sensing and evaluation devices. Elastic nonreciprocity has predominately been studied and demonstrated by active approaches where programmable digital circuits and shunted piezoelectric systems are involved, enabling the coupling of electric energy and mechanical work. Since most of the existing works contributing to elastic nonreciprocity are done based on the introduction of nonlinear interaction or space-time parametric modulation, they inevitably bring about undesired narrow-band operation and modulation tones. To overcome these, we propose a one-dimensional non-Hermitian elastic meta-beam enabled by non-local feedback interactions through periodic piezoelectric patches controlled by programmable digital circuits, to demonstrate the breaking of reciprocity in flexural wave propagation in a linear fashion. The proposed one-dimensional system produces nonreciprocity as well as complex dispersion relations for flexural wave propagation, featuring effective mechanical gain and loss for flexural waves along specific propagation directions. We realize the one-dimensional piezoelectric-based meta-beam by distributing periodically interlaced piezoelectric sensor-actuator pairs connected by programmable digital circuits. The Sensor and actuator of each of the sensor-actuator pairs are separated by a tunable subwavelength distance, exhibiting controllable mechanical energy transport between opposite propagation directions in a nonreciprocal fashion. We show that the proposed meta-beam breaking spatial symmetry generates a favored flexural wave propagation direction due to the fact that one-way instantaneous flexural transmission is enabled by the programmable digital network that performs certain transfer function. To fully investigate and interpret the proposed piezoelectric meta-beam system, we deliver a complete theoretical study on the sensor-actuator pair serving as the building block. We first start with the continuous non-local meta-beam with effective parameters representing the arrangement of distributed sensor-actuator pairs. Traditional transfer matrix method is then utilized to analyze the scattering properties of the sensor-actuator pair as well as its dispersion relations under different selected geometric and electric parameters. Based on the Floquet Bloch theorem, the complex dispersion relations can then be analytically determined. The calculated dispersion relations show that positive and negative wave numbers are locked to specific propagation directions, indicating that the flexural wave transmitted through the meta-beam undergoes attenuation or amplification along certain directions. Numerical simulations based on finite element method are then carried out to further validate the theoretical validation. Our work shows that the feedback control featuring non-local properties in elastic systems could pave the way for further studies on the physics and application of non-Hermitian mechanical systems.</p>

Nonreciprocal Elastic Wave Propagation Through a Non-Local Piezoelectric Meta-Beam

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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