Superscattering of plate bending wave
View Patent ↗Devices for superscattering a plate bending wave include a solid plate, and a circular array of spring-mass resonators positioned on a surface of the plate. All resonators in the circular array have a resonance frequency that can be matched to a frequency of a target flexural wave. The circular array has a diameter that can further be matched to the wavelength of the target flexural wave. Scattering efficiencies can exceed several multiples of the theoretical limit.
1. A device for superscattering a flexural wave, the device comprising:
a plate; and
a circular array of spring-mass resonators positioned on the plate, the array having N degrees of rotational symmetry about a center point, where N is the number of resonators in the array.
2. The device as recited in claim 1 , wherein N is six.
3. The device as recited in claim 1 , wherein the plate has a minimum lateral dimension that is equal to or greater than six-times a diameter defined by the circular array of spring-mass resonators.
4. The device as recited in claim 1 , wherein each spring-mass resonator comprises:
a spring portion connected to the plate and formed of a resilient element having a spring constant, k; and
a mass portion supported by the spring portion and having a mass, m,
wherein each spring-mass resonator has a resonance frequency, f 0 , according to an equation:
f
0
=
1
2
π
k
m
,
and each spring-mass resonator of the plurality has substantially the same resonance frequency.
5. The device as recited in claim 4 , wherein each resonator of the circular array has substantially the same spring constant, k, and mass, m.
6. The device as recited in claim 1 , wherein each resonator of the circular array is substantially identical.
7. The device as recited in claim 1 , comprising a flexural wave source positioned on the plate at a distance from the circular array, and operable to generate a target flexural wave having wavelength, A, such that the target flexural wave propagates from the flexural wave source to the circular array, defining a propagation direction.
8. The device as recited in claim 7 , wherein each resonator of the circular array has a resonance frequency, f 0 , that corresponds to the wavelength, λ, of the target flexural wave by an equation:
λ
=
2
π
D
ρ
t
(
2
π
f
0
)
2
4
,
wherein ρ is plate density, t is plate thickness, and D is plate bending stiffness.
9. The device as recited in claim 7 , wherein the circular array defines a diameter, d, that is substantially equal to λ/2.
10. The device as recited in claim 7 , wherein the plate has a width, w, perpendicular to the propagation direction, the width being greater than or equal to 3λ.
11. A vehicle having a device for superscattering a flexural wave, the vehicle comprising:
a structural plate of the vehicle; and
a circular array of spring-mass resonators positioned on the plate, the array having N degrees of rotational symmetry about a center point, where N is the number of resonators in the array.
12. The vehicle as recited in claim 11 , wherein the structural plate is a floorboard.
13. The vehicle as recited in claim 11 , wherein the structural plate is a floor of an engine compartment.
14. The vehicle as recited in claim 11 , wherein the structural plate is a truck bed.
15. The vehicle as recited in claim 11 , wherein N is six.
16. The vehicle as recited in claim 11 , wherein the plate has a minimum lateral dimension that is equal to or greater than six-times a diameter defined by the circular array of spring-mass resonators.
17. The vehicle as recited in claim 11 , wherein each spring-mass resonator comprises:
a spring portion connected to the plate and formed of a resilient element having a spring constant, k; and
a mass portion supported by the spring portion and having a mass, m,
wherein each spring-mass resonator has a resonance frequency, f 0 , according to an equation:
f
0
=
1
2
π
k
m
,
and each spring-mass resonator of the plurality has substantially the same resonance frequency.
18. The vehicle as recited in claim 17 , wherein each resonator of the circular array has substantially the same spring constant, k, and mass, m.
19. The vehicle as recited in claim 11 , wherein each resonator of the circular array is substantially identical.
20. The vehicle as recited in claim 11 , comprising a flexural wave source positioned on the plate at a distance from the circular array, and operable to generate a target flexural wave having wavelength, λ, such that the target flexural wave propagates from the flexural wave source to the circular array, defining a propagation direction.