Flexural wave absorbers for wave and vibration isolation in thin walled structures
A flexural wave absorber includes a metasurface with an inner portion, an outer portion, and a plurality of beam strips extending between the inner portion and the outer portion. The metasurface also includes a plurality of coupled resonators disposed on the plurality of beam strips. The plurality of coupled resonators can include a lossy resonator and a lossless resonator, two lossy resonators and a lossless resonator, or a lossy resonator and two lossless resonators. In addition, each of the plurality of beam strips can have multiple pairs of coupled resonators disposed thereon that work at or absorb different frequency ranges.
1. A flexural wave absorber comprising:
a metasurface with an inner portion rigidly attached to a thin wall structure, an outer portion free to vibrate, a plurality of beam strips extending between the inner portion and the outer portion, and a plurality of vacant spaces extending through the metasurface between respective adjacent beam strips of the plurality of beam strips; and
a plurality of coupled resonators disposed directly on the plurality of beam strips, the coupled resonators spaced apart by a predefined distance equal to 0.2λ, where λ equals a flexural wave wavelength at a resonant frequency propagating along the plurality of beam strips.
2. The flexural wave absorber according to claim 1 , wherein the plurality of coupled resonators comprise a lossy resonator and a lossless resonator on each of the plurality of beam strips.
3. The flexural wave absorber according to claim 1 , wherein the plurality of coupled resonators comprise two lossy resonators and a lossless resonator on each of the plurality of beam strips.
4. The flexural wave absorber according to claim 1 , wherein the inner portion is an inner circular disc.
5. The flexural wave absorber according to claim 1 , wherein the outer portion is an outer circular ring and the inner portion is an inner circular disc.
6. The flexural wave absorber according to claim 1 , wherein the plurality of beam strips are mechanically coupled to the inner portion and the outer portion.
7. The flexural wave absorber according to claim 1 , wherein the inner portion, the outer portion, and the plurality of beam strips are a monolithic structure.
8. The flexural wave absorber according to claim 1 , wherein the plurality of coupled resonators each comprise two lossy resonators and a lossless resonator and the metasurface is configured to absorb flexural waves independent of direction of incidence.
9. The flexural wave absorber according to claim 8 , wherein the metasurface absorbs greater than 80% of a 0.2ƒ o frequency range of the flexural waves where
f
o
=
1
2
π
k
o
/
m
o
,
k o is the spring constant of each of the two lossy resonators and the lossless resonator, and m o =mass of each of the two lossy resonators and the lossless resonator.
10. The flexural wave absorber according to claim 1 , wherein the plurality of coupled resonators each comprise a lossy resonator and two lossless resonators and the metasurface is configured to asymmetrically absorb flexural waves propagating in a first direction.
11. The flexural wave absorber according to claim 10 , wherein the metasurface absorbs greater than 95% of an 0.15ƒ 0 frequency range of the flexural waves propagating in the first direction, where
f
o
=
1
2
π
k
o
/
m
o
,
k o the spring constant of each of the lossy resonator and the two lossless resonators, and m o =mass of each of the lossy resonator and the two lossless resonators.
12. The flexural wave absorber according to claim 1 , wherein the outer portion is rigidly attached to a panel and the inner portion is free to vibrate independent of the panel.
13. The flexural wave absorber according to claim 1 , wherein the inner portion is rigidly attached to a panel and the outer portion is free to vibrate independent of the panel.
14. The flexural wave absorber according to the claim 1 , wherein the metasurface is a plurality of metasurfaces disposed on a surface, each of the plurality of metasurfaces comprising the inner portion, the outer portion, the plurality of beam strips extending between the inner portion and the outer portion, and the plurality of coupled resonators disposed on the plurality of beam strips.
15. The flexural wave absorber according to claim 14 , wherein:
the plurality of metasurfaces comprises a first subset of metasurfaces configured to absorb greater than 95% of a first frequency range of flexural waves equal to 0.15ƒ 01 for and propagating in a first direction;
a second subset of metasurfaces configured to absorb greater than 95% of a second frequency range of flexural waves equal to 0.15ƒ 02 and propagating in the first direction, where the second frequency range is not equal to first frequency range;
f
o
1
=
1
2
π
k
o
1
/
m
o
1
,
k o1 is the spring constant of each resonator in the first subset of metasurfaces, and m o1 is mass of each of the resonators in the first subset of metasurfaces; and
f
o
2
=
1
2
π
k
o
2
/
m
o
2
,
k o2 is the spring constant of each resonator in the second subset of metasurfaces, and m o2 is mass of each of the resonators in the second subset of metasurfaces.
16. A flexural wave absorber comprising:
a metasurface with an inner portion rigidly attached to a thin wall structure, an outer portion free to vibrate, a plurality of beam strips extending between the inner portion and the outer portion, and a plurality of vacant spaces extending through the metasurface between respective adjacent beam strips of the plurality of beam strips; and
a lossy resonator and a lossless resonator disposed on each of the plurality of beam strips, the lossy resonator and the lossless resonator spaced apart by a predefined distance equal to 0.2λ, where λ equals a flexural wave wavelength at a resonant frequency propagating along the plurality of beam strips.
17. The flexural wave absorber according to claim 16 further comprising another lossy resonator disposed on each of the plurality of beam strips.
18. The flexural wave absorber according to claim 16 further comprising another lossless resonator disposed on each of the plurality of beam strips.
19. A flexural wave absorber comprising:
a plurality of metasurfaces attached to a panel, the plurality of metasurfaces each comprising an inner portion rigidly attached to the panel, an outer portion free to vibrate, a plurality of beam strips extending between the inner portion and the outer portion, a plurality of vacant spaces extending through the plurality of metasurfaces between respective adjacent beam strips of the plurality of beam strips, and a lossy resonator and a lossless resonator disposed directly on each of the plurality of beam strips, the lossy resonator and the lossless resonator spaced apart by a predefined distance equal to 0.2λ, where λ equals a flexural wave wavelength at a resonant frequency propagating along the plurality of beam strips.
20. The flexural wave absorber according to claim 19 further comprising another resonator disposed on each of the plurality of beam strips, the another resonator selected from the group consisting of an another lossy resonator and an another lossless resonator.