Systems and methods for directing flexural waves
Disclosed are systems for directing flexural waves acting upon a structure. In one example, a system includes a beam and a pair of scatterers disposed on the beam and configured to induce a flexural wave on the beam when actuated at a frequency. The system is configured to direct a direction of travel of the flexural wave acting on the beam based on the width of the beam, the distance between the scatterers forming the pair of scatterers, and/or a phase difference between the actuation of the pair of scatterers.
1 . A system comprising:
a beam;
a pair of scatterers disposed on the beam and configured to induce a flexural wave on the beam when actuated at a frequency;
wherein the system is configured to direct a direction of travel of the flexural wave acting on the beam based on at least one of a width of the beam, a distance between the scatterers forming the pair of scatterers, and a phase difference between an actuation of the pair of scatterers; and
wherein the phase difference between the actuation of the pair of scatterers is such that one of the scatterers forming the pair of scatterers is actuated at a 90-degree phase difference from the other.
2 . The system of claim 1 , wherein the flexural wave travels in a first direction along a length of the beam when the phase difference between the actuation of the pair of scatterers is −90 degrees and travels in a second direction along the length of the beam when the phase difference between the actuation of the pair of scatterers is +90 degrees.
3 . The system of claim 2 , wherein the first and second directions are substantially opposite directions.
4 . The system of claim 1 , wherein the pair of scatterers are disposed along a length of the beam.
5 . The system of claim 1 , wherein the distance between the scatterers forming the pair of scatterers is approximately one-quarter of a wavelength of the flexural wave.
6 . The system of claim 1 , wherein a width of the beam is approximately
1
2
of a wavelength of the flexural wave acting on the beam.
7 . The system of claim 1 , wherein at least one of the scatterers forming the pair of scatterers comprises:
a pair of supports;
a flexible material extending between the pair of supports; and
a mass connected to the flexible material.
8 . The system of claim 7 , wherein at least one of the scatterers forming the pair of scatterers further comprises a rigid cross bar extending between the supports forming the pair of supports.
9 . The system of claim 1 , wherein at least one of the scatterers forming the pair of scatterers comprises:
a solid member acting as a mass; and
a flexible member attached to a side of the solid member, the flexible member acting as a spring and damper.