System for absorbing flexural waves acting upon a structure
View Patent ↗Described are systems for absorbing flexural waves acting on a structure. In one example, the system includes a first resonator connected to a structure at a first location and a second resonator connected to the structure at a second location. The distance between the first location and the second location is based on a frequency of a flexural wave acting upon the structure and an orientation of the first resonator and the second resonator with respect to each other.
1. A system comprising:
a first cantilever resonator connected to a flat side of a single beam at a first location;
a second cantilever resonator connected to the flat side of the single beam at a second location; and
wherein a distance between the first location and the second location extends along a length of the flat side of the single beam and is expressed as aλ, wherein λ is a wavenumber at a frequency of a flexural wave to be absorbed and α is 0.02 when the first and second cantilever resonators face away from each other and is 0.2 when the first and second cantilever resonators face toward each other.
2. The system of claim 1 , wherein:
the first cantilever resonator includes a first support base and a first cantilever member that extends in a first direction from the first support base and terminates in a first terminal end; and
the second cantilever resonator includes a second support base and a second cantilever member that extends in a second direction from the second support base and terminates in a second terminal end.
3. The system of claim 2 , wherein an orientation of the first cantilever resonator and the second cantilever resonator with respect to each other is such that the first direction that the first cantilever member extends from the first support base substantially opposes the second direction that the second cantilever member extends from the second support base.
4. The system of claim 3 , wherein the first terminal end and the second terminal end are separated by a distance that is less than the distance between the first location and the second location.
5. The system of claim 3 , wherein the first terminal end and the second terminal end are separated by a distance that is greater than the distance between the first location and the second location.
6. The system of claim 1 , wherein the first cantilever resonator and the second cantilever resonator have resonant frequencies substantially similar to the frequency of the flexural wave acting upon the single beam.
7. The system of claim 6 , wherein the first cantilever resonator is a lossy resonator and the second cantilever resonator is a lossless resonator.
8. A system comprising:
a top set of cantilever resonators connected to a flat top side of a single beam, the top set of cantilever resonators separated from each other by a distance along a length of the flat top side of the single beam; and
a bottom set of cantilever resonators connected to a flat bottom side of the single beam, the bottom set of cantilever resonators separated from each other by the distance along a length of the flat bottom side of the single beam; and
wherein the distance is expressed as aλ, wherein λ is a wavenumber at a frequency of a flexural wave to be absorbed and α is 0.02 when the top set of cantilever resonators face away from each other and is 0.2 when the top set of cantilever resonators face toward each other.
9. The system of claim 8 , wherein resonators forming at least one of the top set of cantilever resonators and the bottom set of cantilever resonators comprise:
a first cantilever resonator having a first support base and a first cantilever member that extends in a first direction from the first support base and terminates in a first terminal end, the first support base being connected to the single beam at a first location;
a second cantilever resonator having a second support base and a second cantilever member that extends in a second direction from the second support base and terminates in a second terminal end, the second support base being connected to the single beam at a second location.
10. The system of claim 9 , wherein an orientation of the first cantilever resonator and the second cantilever resonator with respect to each other is such that the first direction that the first cantilever member from the first support base is such that it substantially opposes the second direction that the second cantilever member from the second support base.
11. The system of claim 9 , wherein the first cantilever resonator and the second cantilever resonator have resonant frequencies substantially similar to the frequency of the flexural wave acting upon the single beam.
12. The system of claim 9 , wherein the first cantilever resonator is a lossy resonator and the second cantilever resonator is a lossless resonator.
13. A system comprising:
a first set of cantilever resonators connected to a single beam, the first set of cantilever resonators separated from each other at a first distance along a length of the single beam, wherein the distance is expressed as aλ, wherein λ is a wavenumber at a first frequency of a first flexural wave to be absorbed and α is 0.02 when the first set of cantilever resonators face away from each other and is 0.2 when the first set of cantilever resonators face toward each other; and
a second set of cantilever resonators connected to the single beam, the second set of cantilever resonators separated from each other at a second distance along the length of the single beam based on a second frequency of a second flexural wave acting upon the single beam and an orientation of the second set of cantilever resonators with respect to each other.
14. The system of claim 13 , wherein cantilever resonators forming at least one of the first set of cantilever resonators and the second set of resonators comprise:
a first cantilever resonator having a first support base and a first cantilever member that extends in a first direction from the first support base and terminates in a first terminal end, the first support base being connected to the single beam at a first location; and
a second cantilever resonator having a second support base and a second cantilever member that extends in a second direction from the second support base and terminates in a second terminal end, the second support base being connected to the single beam at a second location.
15. The system of claim 13 , wherein:
cantilever resonators forming the first set of cantilever resonators have resonant frequencies substantially similar to the first frequency of the first flexural wave acting upon the single beam; and
cantilever resonators forming the second set of cantilever resonators have resonant frequencies substantially similar to the second frequency of the second flexural wave acting upon the single beam.