Abstract
Willis materials exhibit macroscopic cross-coupling between particle velocity and stress as well as momentum and strain. However, Willis coupling coefficients designed so far are intrinsically coupled, which inhibits their full implementation in structural dynamic applications. This work presents a means to eliminate these limitations by introducing an active scatterer in a mechanical meta-layer that exploits piezoelectric sensor–actuator pairs controlled by digital circuits. We experimentally demonstrate abilities of the Willis meta-layer, in beams and plates, for independently engineering transmission and reflection coefficients of flexural waves in both amplitude and phase and nonreciprocal wave propagations. The meta-layer is described by a flexural wave polarizability tensor, which captures independent higher-order symmetric-to-symmetric and symmetric-to-antisymmetric couplings. The active meta-layer is adaptive in real time for reconfigurable broadband operation thanks to its programmability. This work sheds a new light on unsurpassed control of elastic waves, ranging from vibration protections to ultrasonic sensing and evaluation of engineering structures.
Highlights
Willis materials exhibit macroscopic cross-coupling between particle velocity and stress as well as momentum and strain
Mechanical Willis materials exhibit coupling between particle velocity and stress as well as momentum and strain. This coupling has been an emergent effective material property that results from subwavelength asymmetry and/or long-range order[12], which is in agreement with predictions from homogenization theory in elastodynamics[13,14]
The stress–velocity and momentum–strain coupling offered by Willis materials provides appealing solutions in many applications including but not limited to perfect elastic wave cloaking[25], independent control of transmissions and reflections[17], perfect wavefront manipulations[19], and reciprocity breaking[12,16]
Summary
Willis materials exhibit macroscopic cross-coupling between particle velocity and stress as well as momentum and strain. Mechanical Willis materials exhibit coupling between particle velocity and stress as well as momentum and strain In acoustics, this coupling has been an emergent effective material property that results from subwavelength asymmetry and/or long-range order[12], which is in agreement with predictions from homogenization theory in elastodynamics[13,14]. The coupling constants are intrinsically connected, posing fundamental constraints on applications for Willis materials such as broadband operation, violation of reciprocal propagation, and independent and non-conservative control of wave transmission and reflection[12,17]. We present exploration of the ability of an active mechanical Willis meta-layer to realize independent control of the transmission and reflection of flexural waves in beams and plates and break reciprocity (Fig. 1). This is achieved using independently activated symmetric and antisymmetric scattered fields, such that the wave fields in the left and right sides of the Mechanical Willis meta-layer
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