Bender bar transducer with at least three resonance modes
A bender bar acoustic transducer capable of exciting at least three resonance modes is provided. The provided bender bar acoustic transducer may be capable of exciting a second resonance mode by configuring a first portion of a piezoelectric element to contract while a second portion of the piezoelectric element expands when voltage is applied to electrodes coupled to the piezoelectric element. The bender bar acoustic transducer may be further configured such that the first portion and the second portion of the piezoelectric element both contract and/or expand to excite a first resonance mode. The bender bar acoustic transducer may be used in downhole and well logging applications.
1. An acoustic transducer, comprising:
a substrate element;
a first piezoelectric element coupled to a first side of the substrate element, the first piezoelectric element comprising a first portion having a set of electrodes and a second portion having a set of electrodes;
a second piezoelectric element coupled to a second side of the substrate element, the second piezoelectric element comprising a first portion having a set of electrodes and a second portion having a set of electrodes; and
a voltage source coupled to the first and second piezoelectric element to provide:
application of a first alternating voltage to the acoustic transducer to thereby drive the acoustic transducer to vibrate at a first and third resonance mode that are symmetric with respect to a central plane that passes through the first and second piezoelectric elements; and
application of a second anti-phase voltage to the acoustic transducer to thereby drive the acoustic transducer to vibrate at a second resonance mode having a frequency between the first and third resonance modes and that is asymmetric with respect to the central plane, the second anti-phase voltage having an anti-phase component of the first alternating voltage.
2. The acoustic transducer of claim 1 , wherein:
application of the first alternating voltage to the first portion of the first piezoelectric element causes a first stress on the first portion of the first piezoelectric element;
application of the second anti-phase voltage to the second portion of the first piezoelectric element causes a second stress on the second portion of the first piezoelectric element;
application of the first alternating voltage to the first portion of the second piezoelectric element causes the second stress on the first portion of the second piezoelectric element; and
application of the second anti-phase voltage to the second portion of the second piezoelectric element causes the first stress on the second portion of the second piezoelectric element.
3. The acoustic transducer of claim 1 , wherein the substrate element comprises fixed ends.
4. The acoustic transducer of claim 1 , wherein the second portion of the first piezoelectric element comprises a third piezoelectric element and the second portion of the second piezoelectric element comprises a fourth piezoelectric element.
5. The acoustic transducer of claim 4 , wherein application of the first alternating voltage to the first, the second, the third, and the fourth piezoelectric elements cause the acoustic transducer to vibrate to produce at least the first and third resonance modes.
6. The acoustic transducer of claim 1 , wherein:
the first portion and the second portion of the first piezoelectric element are defined by a first partition in a first electrode coupled to the first piezoelectric element, the first partition being a separation extending partially into the first piezoelectric element; and
the first portion and the second portion of the second piezoelectric element are defined by a second partition in a second electrode coupled to the second piezoelectric element, the second partition being a separation extending partially into the second piezoelectric element.
7. The acoustic transducer of claim 6 , wherein:
the second portion of the first piezoelectric element has a different polarization than the first portion; and
the second portion of the second piezoelectric element has a different polarization than the first portion of the second piezoelectric element.
8. The acoustic transducer of claim 7 , wherein the second anti-phase voltage comprises a same phase component of the first voltage.
9. The acoustic transducer of claim 1 , wherein application of the first alternating voltage to the second portion of the first piezoelectric element and the second portion of the second piezoelectric element cause the acoustic transducer to vibrate to produce at least the first and third resonance modes.
10. The acoustic transducer of claim 1 , wherein the first piezoelectric element and the second piezoelectric element comprise at least one of lead zirconate titanate (PZT), barium titanate (BaTiO 3 ), gallium orthophosphate (GaPO 4 ), tourmaline, and quartz and wherein the substrate element is formed of a non-piezoelectric material.
11. The acoustic transducer of claim 1 , wherein at least one electrode of the first portion of the first piezoelectric element is different from at least one electrode of the second portion of the first piezoelectric element.
12. The acoustic transducer of claim 1 , wherein at least one electrode of the first portion of the second piezoelectric element is different from at least one electrode of the second portion of the second piezoelectric element.
13. The acoustic transducer of claim 1 , wherein at least one electrode of the first portion of the first piezoelectric element is the same as at least one electrode of the second portion of the first piezoelectric element.
14. The acoustic transducer of claim 1 , wherein at least one electrode of the first portion of the second piezoelectric element is the same as at least one electrode of the second portion of the second piezoelectric element.
15. A method utilizing an acoustic logging tool within a borehole, the method comprising:
deploying the acoustic logging tool into the borehole;
application of a first alternating voltage to the acoustic logging tool to thereby drive the acoustic logging tool to vibrate at a first and third resonance mode that are symmetric with respect to a central plane that passes through an acoustic transducer of the acoustic logging tool;
application of a second anti-phase voltage to the acoustic logging tool to thereby drive the acoustic logging tool to vibrate at a second resonance mode having a frequency between the first and third resonance modes and that is asymmetric with respect to the central plane;
using at least the first, second, or third resonance modes of the acoustic logging tool to produce an acoustic force along the borehole; and
processing a received acoustic response to the produced acoustic force to determine properties of formations surrounding the borehole.
16. The method of claim 15 , wherein deploying the acoustic logging tool comprises deploying an acoustic logging tool comprising:
a substrate element;
a first piezoelectric element coupled to a first side of the substrate element, the first piezoelectric element comprising a first portion having a set of electrodes and a second portion having a set of electrodes; and
a second piezoelectric element coupled to a second side of the substrate element, the second piezoelectric element comprising a first portion having a set of electrodes and a second portion having a set of electrodes.
17. The method of claim 16 , wherein exciting at least a first, second, and third resonance modes of the acoustic logging tool comprises:
applying the first alternating voltage to the first portion and the second portion of the first piezoelectric element and the first portion and the second portion of the second piezoelectric element; and
applying the second anti-phase voltage to the second portion of the first piezoelectric element and the second portion of the second piezoelectric element.
18. The method of claim 15 , wherein deploying the logging tool comprises deploying the logging tool on a wireline.
19. The method of claim 15 , wherein deploying the logging tool comprises deploying the logging tool coupled to a drill string.
20. A method of utilizing an acoustic transducer comprising:
applying a first alternating voltage to a first portion of a first piezoelectric element of the acoustic transducer to cause a first stress on the first portion of the first piezoelectric element;
applying a second anti-phase voltage to a second portion of a first piezoelectric element to cause a second stress on the second portion of the first piezoelectric element, the second anti-phase voltage having an anti-phase component of the first alternating voltage;
applying the first alternating voltage to a first portion of a second piezoelectric element to cause the second stress on the first portion of the second piezoelectric element; and
applying the second anti-phase voltage to a second portion of a second piezoelectric element to cause the first stress on the second portion of the second piezoelectric element,
wherein the acoustic transducer is driven to vibrate at a first and third resonance mode that are symmetric with respect to a central plane that passes through the acoustic transducer and at a second resonance mode that is asymmetric with respect to the central plane.
21. The method of claim 20 , wherein application of the first alternating voltage to the first and second portions of the first piezoelectric element and to the first and second portions of the second piezoelectric element cause the acoustic transducer to vibrate to produce at least a first resonance mode and a third resonance mode.
22. The method of claim 20 , wherein:
the second portion of the first piezoelectric element has a different polarization than the first portion; and
the second portion of the second piezoelectric element has a different polarization than the first portion of the second piezoelectric element.
23. The method of claim 22 , wherein the second anti-phase voltage comprises a same phase component of the first voltage.
24. A method of utilizing an acoustic transducer comprising:
bending a surface of a piezoelectric transducer in a first direction by applying a first alternating voltage to a first piezoelectric element disposed on said surface and by applying a second anti-phase voltage to a second piezoelectric element disposed on said surface,
wherein the acoustic transducer is driven to vibrate at a first and third resonance mode that are symmetric with respect to a central plane that passes through the acoustic transducer and at a second resonance mode that is asymmetric with respect to the central plane, the second resonance mode having a frequency between the first and third resonance modes.
25. The method of claim 24 , further comprising:
identifying at least a first and second resonant frequency for the piezoelectric transducer;
exciting the transducer at each of the frequencies to bend a surface of the transducer in a first direction, wherein exciting the transducer comprises:
at the first frequency, applying the first alternating voltage to the first piezoelectric element disposed on said surface and the second piezoelectric element disposed on said surface; and
at the second frequency, applying the first alternating voltage to the first piezoelectric element disposed on said surface and applying a second anti-phase voltage to the second piezoelectric element disposed on said surface.