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11/21/2016 Final Report 01 Jan 2013 - 30 June 2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER

Multi-Resonance Shear Mode Transducers

Sb. GRANT NUMBER

N00014-13-1-0258

Sc. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) Sd. PROJECT NUMBER

Richard J. Meyer, Jr. 20733

Se. TASK NUMBER

Sf. WORK UNIT NUMBER

09730 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

Applied Research Laboratoi)t REPORT NUMBER

The Pennsylvania State University P.O. Box 30 State College, PA 16804 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

Jan Lindberg and Mike Wardlaw ONR Office of Naval Research Code 321MS 11. SPONSOR/MONITOR'S REPORT

875 N. Randolph Street NUMBER(S)

Arlington , VA 22203 12. DISTRIBUTION/AVAILABILITY STATEMENT

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Crystallographic engineering of single crystal relaxor-based ferroelectrics was used to design broadband, compact, high power, low frequency transducers. A unique face shear-mode produces a d36 coefficient that has demonstrated the ability provide a robust projector that meets these qualifications. This work looks at expanding the operating bandwidth and/or acoustic power output that may be achieved by designing multi-mode transducers using multiple d36 crystal geometries or combinations of d36 and other crystal cuts.

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a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT

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18. NUMBER OF PAGES

24

19a. NAME OF RESPONSIBLE PERSON

Richard J. Meyer, Jr. 19b. TELEPHONE NUMBER (Include area code)

814-865-9607

Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18

.. . '

DISTRIBUTION STATEMENT A

Multi-Resonance Shear Mode Transducers

Grant: N00014-13-1-0258 Start Date: 01 Jan 2013 End Date: 30 Jun 2016

Principal Investigator: Richard J. Meyer Jr.

PENN STATE

Final Report 21 November 2016

lliJ Applied Re;earch Laboratory

Submitted to:

Jan Lindberg and Mike Wardlaw ONR Code 321 MS

875 N Randolph Street Arlington , VA 22203

Submitted by:

The Pennsylvania State University Applied Research Laboratory

P.O. Box 30 State College, PA 16804-0030

R. J. Meyer Jr. (814) 865-9607

rjmlSO@arl.psu .edu

' '

Multi-Resonance Shear Mode Transducers Prepared by: Douglas Markley

LONG-TERM GOALS

The long-term goals of this effort were to develop a family of transducer designs that utilize the d36 shear piezoelectric coefficient, which has advantages for compact low frequency sonar transducers. The d36 cut is unique in that large electric fields can be applied without depolarization. The d36 mode of operation allows for packaging of a transducer motor section that is unlike any other and therefore a new design space is offered to the designer. This effort looks specifically at designing a d36 transducer that has multiple resonances in order to expand the useful transmit frequency bandwidth.

OBJECTIVES

The primary technical objective was to exploit crystallographic engineering of single crystal relaxor-based ferroelectrics to design broadband, compact, high power, low frequency transducers. Face shear-mode transducers based on the d36 coefficient have demonstrated the ability to design a robust projector that meets these qualifications. Further expanding the operating bandwidth and/or acoustic power output may be achieved by designing multi-mode transducers using multiple d36 crystal geometries or combinations of d36 and other crystal cuts.

APPROACH

Traditional approaches to compact sonar projector design usually involve mechanical amplification schemes or bending modes of the active material. Structures using mechanical amplification tend to be very narrow band and have low electromechanical coupling coefficients. Bending modes are also traditionally narrow band and generally have long-term reliability issues. While implementing single crystal materials into these structures improves performance, the full electromechanical coupling of the material is still degraded.

Crystallographic engineering in the single crystal lead magnesium niobate-lead titanate (PMNT) system has uncovered a very unique piezoelectric shear mode. Contrary to other more common shear coefficients, this one operates with working electrodes that are the same as the poling electrodes. Therefore, very large driving fields can be applied to the device without depolarization. This mode of operation is not available in conventional piezoceramics. This cut was recently integrated into a sonar transducer design that combines low frequency operation with small packaging and high acoustic output.

There is a significant design space left to explore with this new mode of operation. This study focused on the ability to design multiple resonances into the structure to tailor the performance of the device. Multiple resonances can be combined to improve output or lower the frequency of

operation or can be separated to extend the operating bandwidth of the device. Modeling, both one dimensional and finite element analysis, was used to explore the design space. Prototype designs were fabricated and tested for proof of concept.

The design shown in Figure 1 has d36 mode crystals separated into two motor sections. The components of this design concept include a light/stiffhead mass (dark gray), a heavy tail mass (light gray), d36 crystals (black), and a central mass (cross-hatched). The resonance frequency of each motor section can be controlled through the dimensions (width, height or length) of the crystal plates. In this case, the two motor sections can be combined to lower the resonance frequency (mechanical springs in series) or they can be designed at different frequencies to create a multi-resonant spectrum and thereby increasing the bandwidth of the projector.

Figure 1 Multi-mode transducer; both sections use longitudinal shear crystals. (Left) full transducer with dark gray head, light gray tail, crystals in solid black, and center support in back

cross-hatch. (Right) is a cut-view showing nested head and tail.

WORK COMPLETED

An equivalent circuit model of d36 shear mode transducers was developed to more rapidly explore transducer design space. The model considers a mass-spring-mass-spring-mass system. The model was exercised and compared to results obtained using finite element analysis.

Based on equivalent circuit analysis, final geometries were then modeled using ATILA++ finite element code. Refinements were made to the central mass geometry and materials to produce a desirable frequency response curve.

As an example ofthis process, a dual-shear mode transducer was constructed that measured 1.5 inches in diameter and was 2.75 inches in length. In air impedance sweeps were measured

during each stage of fabrication and compared to model results to ensure fabrication proceeded as expected. A cut-away model and photograph of the finished unit is shown in Figure 2

Part drawings were produced and parts were procured. d36 crystals were obtained from HC Materials. Crystals were inspected, measured, and sorted for use in the transducer design and evaluated for proper motion using a scanning laser vibrometer.

In-air testing was done on the finished unit. These data were compared to model predictions.

Figure 2 Model (1 /4 symmetry) and photograph of the assembled dual stage d36 tonpilz transducer.

In-water testing of the unit was conducted by placing the unit in a single element housing. The unit was tested in water by driving the bottom and top d36 stages in phase and then the lower d36 stages was driven 180° out of phase.

Many other design configurations were explored in modeling studies to take advantage of the unique properties of d36 orientated single crystals. One such design uses an alternate positioning of the crystals and allows for utilizing the d36 mode in an axial direction (free-shear) to build devices similar to classical tonpilz designs. This new approach permits simpler fabrication and allows for the use of pre-stress bolts. Single and Dual-Mode prototypes of this concept were constructed and evaluated.

RESULTS

Figure 3 shows an example of the modeled response curve for the multi-mode d36 prototype in Figure 2. Two d36 shear crystal drivers are configured in series with a center-mass between. The

output is shown when the top and bottom sections are driven in phase. The modeled deflection shapes are also shown. The null in mid-band results when the central mass moves out-of-phase with the head and tail. The motion can be adjusted through design and material choices for the central mass and crystals. The null can also be countered by phasing the drive signals between the top and bottom crystal stages, preventing the phase synchronization. This is shown in Figure 4, where the drive voltage phase of the bottom stage was adjusted relative to the top stage in the models.

40

e 11 0 a

00

90

Transmitting Voltage Response vs Freq

Null

Second Resonance First Resonance

__ ... :.;__ ___ _ 5000

Figure 3 Modeled transmit voltage response showing the fundamental resonance of the device and overtones.

0 soc

Transmitting Voltage Response of Half Size Model

15000

Fr u.ncy

Figure 4 TVR showing the effect of adjusting the drive-phase of the bottom stage relative to the top.

Figure 5 shows the transducer during fabrication. The top and bottom stages were assembled separately and then combined during the final fabrication step. The top and bottom stages were built using the same single crystal geometry. The crystals in the top and bottom stages were sorted to have the most uniform properties within the stages. At each stage of fabrication, the impedance was checked and compared against prediction. Figure 6 shows the impedance of the finished unit in air measured in free conditions and in the housing used for in water testing.

Figure 5 Photos of the bottom and top stages during the fabrication process.

Figure 6 Measured vs. modeled in-air impedance of dual-shear prototype.

In water testing results are shown in Figure 7 and Figure 8. A reasonable match was achieved, in spite of some low frequency noise that was believed to be attributable to spurious modes in the housing structure.

140 ~----------------------.. y---------------------------,

- Model In-Phase

- Measured In-Phase

- Model 180° Phase

- Measured 180° Phase

80 +-------~---L-------------,--------------------------~

I 000 I 0000 I 00000

Log Frequency (Hz)

Figure 7 Measured and modeled TVR of dual-shear prototype.

I 00000 ,-------------------------------------------, 90

- Model In-Phase Model In-Phase

1'\ - Measured In-Phase - Measured In-Phase 60 - Model 180' Phase

- Model 180' Phase 1\ - Measured 180' Phase

- Measured 180' Phase ,...., 30 CD ..

~ .. C'.o

1000

= 0 ~ .. "' ~ -= g.

-30

-60 !J

\..,

~ ~ ~ ~ '-. " 100 +---------------------,-------------------~ -90 1000

b 1000 10000 10000 10000

Log Freq uency (Hz) Log Frequency (Hz)

Figure 8 Measured and modeled in-water impedance and phase of the dual-shear prototype.

The design above has the two crystal drivers in a series configuration. Some other conceptual design variations that were modeled are shown below. These designs provide options that might be adjusted to meet the needs of a variety of applications in terms of acoustic performance, and physical/dimensional design constraints.

r-

100000

In another true series configuration (Figure 9 ) a stack of d33 crystals is located between the shear crystals and the tailmass. This is a quarter symmetry model, so it would actually require four stacks, etc. In this case the center-mass flexes in a rocking motion that is not overcome by phasing the drivers.

170

~ Stack Below "' 160 = 0 Q. 150 "'~ ~ E ~-

140 ~ @) OJ) ~ = "'

• STEEL1 .... "' 130 -:I

0 ALUMINUM1 ~-= . AiurTWla :::~ 120 • PIN24_PMN_PT _rotated s~ • HCPINOOI "' 11 0

llli = = ~ 100

11 ' "'- """'\. ~b ...

1\ ;, ._ ~ \

- ~

I "' --.... I I M J \ \ v

I - Stack Below 0° Phase

I - Stack Below 180° Phase

I 90 0 2 4 6 8 10 12 14 16 18 20

Frequency (kHz)

Figure 9 Dual mode transducer with d33 stacks below the shear section. (1 /4 symmetry shown.)

Figure 10 shows two layers of shear crystals in series, with cantilever motion, to drive a square head. Like the prototype above, this results in an extra low fundamental resonance frequency, doubling the effective length of the crystal section. In the base configuration the preferred motion of the crystals is in opposition, spreading the head and tail masses apart. The out-of­phase coupler mode (;::;3500Hz) fights against the preferred motion and is therefore weak in this case due to the stiffuess of the crystals. Note the change in behavior when the drive polarity is altered. By reversing the polarity of one set of crystals the two layers of crystal prefer to move in parallel, and a synergistic mode is formed that releases a fuller motion of the coupler. The counter balancing of the main body against the motion of the coupler causes vibration in the head for a second mode. If the drive phase is switched at the appropriate frequency during a sweep, the resulting TVR will show two peaks.

Figure 11 shows a similar concept, only this time the center mass is "Folded" back under one of the stacks for smaller cross-sectional dimensions. It too shows very low resonance frequency and strong effects from polarity reversals, showing two peaks with polarity reversal.

Figure 12 illustrates a means of achieving broad-band response by driving the devices with different polarities through different frequency ranges.

150

~

"' Square Dual Shear

= 140 0 c. "'~ ~ E ~ - 130 ~ @) Oil> ~ -..

..... Q. 120 - :::l

~-= .t:~ 11 0 · s~

• ALUMINUM1 "' = 0 TUNGSTEN ~ 100 • ALUMINA ~

- 0° Phase

- 180° phase

• PIN24_LOWK_SHE 90 0 5 10 15 20

Frequency (kHz)

Figure 10 Two series layers of shear crystals. (112 symmetry shown.)

170

~

"' 160 = 0 c. 150 "'~ ~ E ~-~ @) 140

: ~ .... Q. 130 - :::l

~-= 120 ..:=~ s~

"' 11 0 = • STEEL1

~

~ 100 0 ALUMINUM1

Folded Design j A

1\ I' ~ rc ~ ~\ I I " -t\ / \ ..

,, \ '

I v I -, l

/j I \(\I ~ fj I'

I - Folded 0° Phase

- Folded 180° Phase • ALUMINA 90 • PIN24 PMN_PT ROTAT~- 0 2 4 6 8 10 12 14 16 18 20

Frequency (kHz)

Figure 11 Dual layer shear design with one layer folded under the other. (1 /4 symmetry shown.)

150

Cl.l

"' = 140 0 Q. "'~ Cl.l Ei

130 ~-Cl.l @)

~ ~ 120 .... ~ - " ~ : ;:: , ~ 9:3.

11 0

"' = ~ 100

~ 90

0

170

Cl.l

"' Folded Design

.I 160 = 0 Q. 150

(\ 1/\, _,./ 1\ "'~ Cl.l Ei ~-

Cl.l @) 140

~ ~ .... ~ 130

~ -= ::: ~ 120 - 0° Phase 9:3. - 180° phase "' 11 0 =

J v ' n / ~ \ 1\

I ~ \ "\ . I I IV\ I

y

~

~ 100 - Folded 0° Phase

- Folded 180° Phase

90 5 10 15 20 0 2 4 6 8 10 12 14 16 18 20

Frequency (kHz) Frequency (kHz)

Figure 12 Increased bandwidth resulting from drive polarity adjustment.

Adjusting the dimensions of the crystal sections allows for tailoring of the results. In Figure 13 a version of the "Square Dual" design is shown where the top row of crystals is 1" X 0.3" X 0.1 ", and the bottom row crystals are 1" X 0.5'' X 0.1 ". Here the upper layer is now somewhat softer and the resulting increased coupler motion can drive the head for a second mode. The 180° voltage phasing drives the coupler mode even more strongly and has some benefit at frequencies above the two main resonances.

... "' =---0 8 ~ ..... ~ @ ~~ "" "" ;:: ~

~ .: .~ QJ

8 ... "'~

• ALU MINUM1 C: "CC "" '-'

D TUNGSTEN ~

• ALU MINA

• PIN24 LOWK SH

160

150

140

130

120

11 0

100 0

- oo Phase

- 180° Phase

10

Freq uency (kHz) 15 20

Figure 13 Square Dual-Shear with reduced width in the upper set of crystals (1 /2 symmetry) .

Another dual-layer cantilever configuration, this time with the bridging mass .in the interior, is shown in Figure 14 together with the TVR results with all in phase or with one layer 180° out of phase with the other. In this case the bridging/coupler mass is an alumina sleeve through which a bolt may pass if desired. As before, reversing the polarity of one section enhances the coupler motion to create a second mode. Again, reducing the width of the upper set of crystals releases the coupler mode sufficiently to allow it to drive the second mode (Figure 15)

160

Q,j

"' = 150 ~ A 0 c. "' ,.-.. Q.l E I \ I

~ ~ ,-........... ) 1\ 1 ~~ 140 Q,j @

Oil> t:-:0!

..... Q.. 130 - = ~-: .-::: ~ 120

• ALUMINUM1 6::!-"' D TUNGSTEN =

• Alumina eo: 110 ~

• PIN241ow

I ~ f-J ' ' ~ 1\...

I ' ~

I \ J - Short Stack Concentric

I l - Short Stack Concentric

J 100 0 5 10 15 20 25 30

Frequency (kHz)

Figure 14 Two layer shear transducer with interior bridge/coupler mass (1 /2 symmetry).

160

Q,j

"' = 150 0 Q. "' ,.-.. Q.l E ~- 140 Q,j @

~~ ... Q.. 130 - = ~-: .......

• ALUMINUM1 ..... = 120 8::!.

D TUNGSTEN "' = eo: 11 0 • Alumina '"' ~ • PIN24 1ow

100 0 5 10 15 20 25 30

Frequency (kHz)

Figure 15 Interior coupled device with reduced width upper crystal layer (1/2 symmetry).

The options discussed above all utilize a series arrangement of the two crystal drivers. Figure 17and Figure 16 Error! Reference source not found. show parallel and series dual mode designs with small cross-sectional profile. These designs also demonstrate the frequency distribution achievable with varying polarity drive. These designs utilize a large volume of crystal, which provides high output power, but they are heavily mass loaded for low­frequency/high Qm peaks.

• ALUMINUM1

0 TUNGSTEN

• AILmlna

• PIN24_1owK

• HCPIN001

Type-B d33 above shear Pseudo-Series with Rigid Coupler

~

"' = 0 Cl.. "'~ ~ e ~ -~ @)

:~ ..... "" - " ~-= ~~ s:::. "' = ~

~

170

160

150

140

130

120

11 0 0 5 10 15

Frequency (kHz)

Figure 16 Series arrangement of d33 and d36 sections in small cross-section (1/4 symmetry).

• ALUMINUM1

D TUNGSTEN

• Alumina

• PIN24 lowK

• HCPIN001

1)rpe-A d33 below shear True Parallel

~

"' = 0 Cl.. "'~ ~ e ~-~ @)

:~ ..... "" - " ~-= ........ ·a~ "' = ~

~

170

160

150

140

130

120

11 0 0 10

Frequency (kHz) 15

20

Figure 17 parallel arrangements of d33 and d36 sections in small cross-section (1 /4 symmetry).

20

Another parallel arrangement is shown in Figure 18 with two independent tail masses each connected to two cantilevered crystals. To achieve the result shown, the upper tailmass is one­half the mass of the lower.

on ~~~--~------~--~~~~----~--~~_J

Figure 18 Two cantilever layers with separate tailmasses (full symmetry) 15

An alternative with wide, short profile can be made using two layers of cantilevered shear crystals nested in series radially, as shown in Figure 19. The combination ofthe crystals with the central mass makes one effective-length armature for extra low frequency. The second mode is a mechanical head flap. Therefore, in this case, 180° phasing gains nothing but actually disrupts the main mode. The third mode is actually the "coupler" mode. Adding more crystals increases the output power and the resonance frequency (Figure 20).

160

~

"' 150 = ~ -Radi a lly Nested Stack I - I 80° Phase difference

0 Q. "' .-. ~ E

140 ~-~ @)

~~ 130 -Q., - " ~-=

:::~ 120 =~ "' = <:IS

~ 11 0

l ' I\_ ~ ~

\__ VI \ 1/ ~

v 'I../

~ IV L/ ~

IV " I ~ 100 0 5 10 15 20 25

Frequency (kHz)

Figure 19 Radially nested shear layers (114 symmetry).

160 - Radially Nested Stack

(!; 'I}

150 = - 2XCrystal

0 c. 'I} ~

(!; a 140 ~-

(!; @)

~~ 130 -!:I. -=

~: ... ;t::CQ 120 s:::. 'I}

= ~

~ 11 0

A

\ jl \ ) / \

1/ 7 \~ ~ \ -\/

" LY ~

"" 100 ' ~

0 5 10 15 20 25

Frequency (kHz)

Figure 20 Radially nested shear layers with 2X crystal volume.

Figure 21 illustrates a possible configuration to use the cantilever motion of the crystals in a "scissoring" motion. The response is very broad band, but as the impedance and phase curves in Figure 22 illustrate, the effect is largely reactive, and results partly from mechanical modes of the headmass.

150

(!; 'I}

140 = 0 Q. "'~ (!; e

130 ~-(!; @)

~~ 120 -!:I.

- = ~-=

• STEEL1 ~~ 110 D ALUMINUM1 s:::.

"' • PIN24 LOWK SH = eo::

~ 100

~ l/ 'I\ N I~ .... '¥'4

___.1'

I I I

90 l 0 5 10 15 20 25 30 35

Frequency (kHz)

Figure 21 Scissor profile shear transducer (112 symmetry).

\

40

60

---- 1--4 30

-30

-60

100 -l---4--=.J---':=*=~~~=+----~=~:...P::::::::::::=J. -90 0 10 15 . 20 25 30 35 40

Frequency (kHz)

Figure 22 In-Water impedance and phase ofthe "Scissor" transducer.

In the course of these investigations, an alternative mechanism was uncovered for using the d36

motion to advantage. Figure 23 shows the loaded "Simple-Shear" motion of a cantilever configuration contrasted with the unconstrained "Free-Shear" motion that results from an unloaded state. In Figure 24 and Figure 25 the crystallographic orientation and resulting displacement motions are shown for what will be referred to as a Free-Shear design. In this

orientation, the elongation motion direction [0 11] can be aligned with the desired device displacement direction, therefore, a stress bolt can be used in the device.

Free-Shear

Figure 23 Simple-Shear and Free-Shear Displacements

"Free-Shear" Polarization Orientation

Free-Shear Displacement

Figure 24 "Free-Shear" crystallographic orientation and displacement model for d36 crystal.

1 Headmass

Head mass

Tail mass Tailmass

Figure 25 Free-Shear transducer concept.

Figure 26 Four-crystal "Free-Shear" tonpilz model (full symmetry).

Figure 26 shows a model of a prototype "Tonpilz" type device using four Free-Shear crystals and a stress bolt.

Part drawings were produced and parts were procured. d36 crystals were obtained from HC Materials. Crystals were inspected, measured, and sorted for use in the transducer and evaluated for proper motion using a scanning laser vibrometer.

A photograph of the assembled prototype appears in Figure 27. The in-air impedance of the assembled device is shown in Figure 28. The modeled impedance is a very good match to the measured, but with a few high Qm spurious modes. The TVR of this "proof-of-concept" design is shown in Figure 29. The result is similar to the model, but contains some spurious modes, some of which were later attributed to modes in the single element housing that was used.

Figure 27 Photograph of Free-Shear prototype assembly.

100,000 .-----------y-------------------,

- Measured

1 0 ~----,----~----~---.-----1

0 20 40 60 Frequency (Hz)

80 100

Figure 28 Measured and modeled in-air impedance of the Free-Shear tonpilz prototype.

1W .----- - - --- - -----------,

150

II>

"' =,-.. :s. 5140 +-----/ .,-~ @) ~?: ~~130 +----7~r-~t--,~--------~l-u-~-+l

~.: .~ ~ 5 ... ;; !;§ 120 +---1 o:l ._,

~

100 -0 5000 10000 15000 20000 (H25000 t ·requency ZJ

30000 35000 40000

Figure 29 Measured and modeled transmit voltage response of the Free-Shear tonpilz prototype.

This configuration was then used to develop a multi-resonant prototype device, with two layers of Free-Shear crystals in series, as shown in Figure 30

Part drawings were produced and parts were procured. d36 crystals were obtained from HC Materials. Crystals were inspected, measured, and sorted for use in the transducer design and evaluated for proper motion using a scanning laser vibrometer.

The in-air impedance of the assembled device is shown in Figure 31. The modeled impedance is a very good match to the measured. The TVR of this "proof-of-concept" design is shown in Figure 32. The result is similar to the model.

Figure 30 Photograph of the dual layer Free Shear tonpilz.

100000 ------------------------,

- 2 - 3

1 00 --------~----~==4======~----1

10 ---------------------------~

0 5.000 10,000 Frequency (Hz)

15.000 20.000

Figure 31 Modeled in-air impedance of the dual-layer Free-Shear tonpilz.

IW ,---~----,-----,--r======================~ - Prototype II Model

- Prototype II Model 180 1so f----+-----t+-----t----'==t===t===F===1F=~

100 ~~~._--~----L---~----~~~UL--~----~

0 10 15 20 25

Frequency (kHz) 30 35 40

Figure 32 Measured and modeled transmit voltage response of the dual-layer Free-Shear tonpilz.

This orientation is sensitive to the alinement of the crystallographic directions with geometries. For example, for the crystal pieces used in the device above a modeling study shows the effects of misalignment of the crystallographic direction. Careful orientation and cutting by the vendor is required.

- Baseline- correct alinement I 00,000 .,.---------,---------,,.---------'--....1 - 10• off

- 90• off

1 00 +--------r~&---_,------~~+Hr-----r------~

10+-------~--L----4--------+-------~------~

0 50 100 150

Frequency (kHz) 200 250

Variations of designs using the Free-Shear orientation have been explored in modeling studies, including scaling effects (Figure 33 and Figure 34) and multi-resonant designs (Figure 35 through Figure 37).

Head Size

Crystal Size

Crystal count

Crystal Volume

Partl

3" X 3"

.75" X .75"X.1"

14

.79 in3

Part2

1.3" X 1.3"

.32" X .32"X.043"

14

0.06 in3

Figure 33 Scaling effects of another Free-Shear tonpilz design.

0 5 10 15 20 25

Frequency (kHz) 30

Figure 34 Transmit voltage response of the scaled Free-Shear tonpilz transducers.

' I

160

Q) - TBSYNI 0 phase

"' 150 = 0 - TBSYNI 180 phase c. "'~ Q) E

140 ~ -Q) @) oti c ~ ..

130 -c. - = ~'; - ... ·a~ 120

"' = ~

~ 11 0

0 ~

~ \ ~ ~ ' r-...

\ ~~ ' A

I 100 I

0 5 10

Frequency (kHz) 15 20

Figure 35 Modeled TVR of a series arrangement of Free-Shear and Simple-Shear section with small cross-section (114 symmetry).

160

Q)

"' = 150 0 c. "'~ Q) E ~- 140 Q) @)

~~ -c. 130 - = ~'; - ... ... ~ 120 =~ "' = ~ 11 0 ~

100 0 5 10 15

Frequency (kHz)

Figure 36 Free- and Simple-Shear components in a multi-resonant design (1 /2 symmetry).

20

170

~

"' = 160 0 Cl. "'~ ~ e ~- 150 ~ @) 1:).();>

~'" ..... =.., 140 - = ~-: -~ ~ 130 a~

• ALUMINUM1 "' = D TUNGSTEN ~ 120 II Alumina ~ • PIN24 LOWK sh 11 0

0 5 10 15

Frequency (kHz)

Figure 37 Multi-resonant stack of Free-Shear crystals (1 /2 symmetry).

IMPACT/ APPLICATIONS

Successful designs of very broad bandwidth transducers that are compact have many applications to Navy sonar.

SUMMARY

Multi-resonance shear designs have been explored using finite element modeling. The design space revealed several configurations of academic interest, including a new "free shear" configuration that has significant potential. Experimental prototyping of these designs confirm model predictions. Additional work is needed to fully vet the potential of these new designs.

20