Mechanical resonating structures and methods

1. A device comprising:

a body;

a substantially rectangular mechanical resonating structure comprising two opposing sides and configured to support in-plane Lamb wave vibration in a direction substantially parallel to the two opposing sides; and

a multi-element anchor coupling the mechanical resonating structure to the body and connected to a side of the mechanical resonating structure, the multi-element anchor comprising a flexible element that is flexible in a direction perpendicular to a direction of vibration of the mechanical resonating structure.

2. The device of claim 1 , wherein the body is a substrate.

3. The device of claim 2 , wherein the mechanical resonating structure is substantially planar.

4. The device of claim 2 , wherein the multi-element anchor comprises a first element proximate the mechanical resonating structure and a second element distal the mechanical resonating structure and contacting the substrate, the second element being the flexible element.

5. The device of claim 4 , wherein the second element is flexible in a direction perpendicular to a direction of vibration of a dominant in-plane vibration mode of the mechanical resonating structure.

6. The device of claim 4 , wherein the first and second elements of the multi-element anchor are oriented substantially perpendicularly to each other.

7. The device of claim 4 , wherein the first element of the multi-element anchor is a beam and has a length approximately equal to a multiple of one quarter of a wavelength of a resonance frequency of vibration of the mechanical resonating structure.

8. The device of claim 4 , wherein the first element of the multi-element anchor is a beam and has a length of less than approximately 5 microns.

9. The device of claim 8 , wherein the first element of the multi-element anchor has a width of less than approximately 5 microns.

10. The device of claim 4 , wherein the first element of the multi-element anchor is a beam and has a width of less than approximately 5 microns.

11. The device of claim 4 , wherein the second element of the multi-element anchor comprises two ends fixed to the substrate, and wherein the second element is flexible between the two ends.

12. The device of claim 11 , wherein the second element of the multi-element anchor is a beam, the beam having a length and width defining a resonance frequency of the beam to be approximately equal to a resonance frequency of the mechanical resonating structure.

13. The device of claim 11 , wherein a length of a flexible portion of the second element is approximately equal to a multiple of ¼ of a wavelength of a resonance frequency of the mechanical resonating structure.

14. The device of claim 13 , wherein the length of the flexible portion of the second element is in the range of approximately 5-50 microns.

15. The device of claim 2 , wherein the mechanical resonating structure has a largest dimension less than approximately 1000 microns.

16. The device of claim 2 , wherein the mechanical resonating structure has a resonance frequency between approximately 1 kHz and 1 GHz.

17. The device of claim 2 , wherein the mechanical resonating structure has a resonance frequency between approximately 1 GHz and 10 GHz.

18. The device of claim 2 , wherein the device comprises two or more multi-element anchors coupling the mechanical resonating structure to the substrate.

19. The device of claim 18 , wherein the device comprises four multi-element anchors coupling the mechanical resonating structure to the substrate.

20. The device of claim 18 , wherein the device comprises six multi-element anchors coupling the mechanical resonating structure to the substrate.

21. A method of operating a substantially rectangular mechanical resonating structure comprising two opposing sides and configured to support in-plane Lamb wave vibration in a direction substantially parallel to the two opposing sides and coupled to a body by a multi-element anchor, the method comprising:

actuating the substantially rectangular mechanical resonating structure so that the substantially rectangular mechanical resonating structure exhibits in-plane Lamb wave vibration with vibration in a primary direction and a secondary direction, the primary direction being substantially parallel to a side of the substantially rectangular mechanical resonating structure and the secondary direction being substantially perpendicular to the primary direction; and

damping the vibration in the secondary direction using a flexible element of the multi-element anchor,

wherein damping the vibration comprises flexing the flexible element of the multi-element anchor in a direction substantially parallel to the secondary direction.

22. The device of claim 4 , wherein the first element of the multi-element anchor is a beam and has a length approximately equal to a multiple of one quarter of a wavelength of a Lamb wave supported by the mechanical resonating structure.

23. The device of claim 2 , wherein corners of the mechanical resonating structure are not anchored.

24. A device comprising:

a substrate;

a substantially rectangular, planar mechanical resonating structure comprising two opposing sides and configured to support in-plane Lamb wave vibration in a direction substantially parallel to the two opposing sides; and

first and second multi-element anchors coupling the mechanical resonating structure to the substrate and connected to respective ones of the two opposing sides of the mechanical resonating structure, each of the first and second multi-element anchors comprising a first element proximate the mechanical resonating structure and a second element distal the mechanical resonating structure and contacting the substrate, the second element being a flexible element that is configured to flex in a direction perpendicular to the direction of the in-plane Lamb wave vibration of the mechanical resonating structure, wherein

the first and second elements of each of the first and second multi-element anchors are oriented substantially perpendicularly to each other.

25. The device of claim 24 , wherein the first element of each first multi-element anchor is a beam and has a length approximately equal to a multiple of one quarter of a wavelength of the in-plane Lamb wave vibration supported by the mechanical resonating structure.

26. The device of claim 25 , wherein the substantially rectangular, planar mechanical resonating structure comprises an active layer comprising a piezoelectric material, and wherein the substantially rectangular, planar mechanical resonating structure further comprises one or more electrodes configured to activate the in-plane Lamb wave vibration via piezoelectric actuation of the active layer.

27. The device of claim 24 , wherein the second element of each multi-element anchor is a beam, the beam having a length and width defining a resonance frequency of the beam to be approximately equal to a resonance frequency of the mechanical resonating structure.

28. The device of claim 24 , wherein a length of a flexible portion of the second element of each multi-element anchor is approximately equal to a multiple of ¼ of a wavelength of a resonance frequency of the mechanical resonating structure.

29. The device of claim 28 , wherein the length of the flexible portion of the second element of each multi-element anchor is in the range of approximately 5-50 microns.