A liquid column resonance (LCR) transducer, also referred to as an organ pipe transducer, is a type of transducer that utilizes the liquid column resonance mode to produce acoustic energy underwater. Traditional transducers, such as piezoelectric rings or Janus transducers, are commonly used as the driving source in LCR transducers. A flextensional transducer (FT) is introduced into the LCR transducer as the driving source because of the relatively larger volume velocity at low frequencies. Moreover, the eigen-mode of the Class IV FT is easier to couple with the LCR mode to broaden the bandwidth of a LCR transducer. To overcome the problems associated with the low stiffness of elliptical metal pipes, an improved aluminum pipe, which has a cross-beam to increase the stiffness, was proposed and utilized in a LCR transducer driven by a Class IV FT. The fabricated LCR transducer prototype driven by the Class IV FT has two resonance peaks from 700–2000 Hz, and the transmitting voltage response values of these peaks are 132.1 and 137.8 dB (re 1 μPa/V @1 m). Comparing with an LCR transducer driven by a 33-mode ring, the results show that the LCR transducer driven by a Class IV FT provides good efficiency and broadband characteristics.

A liquid column resonance (LCR) transducer is a type of underwater acoustic transducer that uses the LCR mode to radiate acoustic energy. LCR transducers have low frequency and operate in deep-water; thus, they can be applied in many fields, such as environmental monitoring,1,2 acoustic tomography,3,4 deep-water geological exploration,5,6 under-ice and long-distance positioning, communications, and navigation.4,7 Traditional transducers are used in LCR transducer as driving sources. Free-flooded rings,8 Janus transducers,9 or spherical drivers4 are the most popular driving sources in typical applications. Bubble resonators have also been applied in LCR transducers to constitute ultra-low frequency seismic sources.10,11

Because of the low-frequency characteristics of the LCR transducer, the driving source, such as a 33-mode ring, usually operates over the bandwidth below its resonance. Thus, the driving source is expected to have a larger volume velocity. Moreover, because the high mechanical Q value of the LCR mode results in a narrow bandwidth,12 a multimode LCR transducer is a solution to extend the bandwidth—there are two approaches to achieve a multimode LCR transducer. The first one is using high-order LCR modes to couple with the 1st order LCR mode, just like the Tonpilz transducer.13 The other approach is using the eigen-mode of the driving source to couple with the 1st LCR mode, which means the eigen-frequency of the driving source is expected to be close enough to the eigen-frequency of the 1st LCR mode.

To increase the efficiency of a LCR transducer and broaden its bandwidth, a LCR transducer driven by a flextensional transducer (FT) is proposed in this paper. FT is a kind of transducer that utilizes the flexural mode of the shell, driven by the longitudinal mode of the piezoelectric stack, to generate vibration energy.14,15 The most common design is the Class IV type, which is an elliptical shell driven by a piezoelectric ceramic stack along the major axis of the shell. Because of the amplitude amplification of the ellipse, a small volume velocity of the piezoelectric stack can be amplified to a larger volume velocity of the elliptical shell, particularly for a frequency band much lower than that of the resonance frequency of the piezoelectric ceramic stack longitudinal mode. In addition, the low-frequency characteristic of a FT is favorable for multimode LCR transducers because the eigenfrequency of the FT is closer to that of the LCR mode compared with that of a piezoelectric ring transducer.

In Sec. II, the problems in the LCR transducer driven by a Class IV FT are described by the finite element model. Due to the low stiffness of elliptical metal pipes, the transmitting voltage response (TVR) of the LCR mode is too low to couple with the mode of FT and the efficiency is too low to show the advantage of the FT driving. Moreover, the flexural modes of elliptical pipes inhibit the coupling between the LCR mode and the flexural mode of the FT. To overcome these problems, an improved metal pipe with a higher stiffness is proposed in Sec. III.

The influences of FT structural parameters are displayed in Sec. IV. Section V describes the development and analysis of the multimode LCR transducer prototype driven by a FT with improved aluminum pipes. The measurement and simulation results were in good agreement. The results indicate the LCR transducer driven by a FT is a promising low-frequency, deep-water, high-efficiency, broadband underwater acoustic transducer.

The structure of the LCR transducer driven by a Class IV FT is illustrated in Fig. 1. Two elliptical metal pipes (front and back pipes) are located on both sides of the Class IV FT driving source. Two pieces of isolation (brown regions in Fig. 1), which are made of cork, are located at both sides of the FT shell to decouple the vibration between the pipes and the FT shell. The isolation fills the gaps between the pipes and the FT shell to prevent the water inside flowing out from these gaps. There is an elliptical hole in each piece of isolation to allow the water to flow freely inside the transducer. Because the water can only flow out from the upper and bottom openings of the transducer, the water inside constitutes elliptical-section longitudinal liquid column resonator.

FIG. 1.

(Color online) Structure of the LCR transducer driven by the Class IV FT. (a) The section of the elliptical tube. (b) The section of the Class IV FT. The elliptical tubes are located on both sides of the FT.

FIG. 1.

(Color online) Structure of the LCR transducer driven by the Class IV FT. (a) The section of the elliptical tube. (b) The section of the Class IV FT. The elliptical tubes are located on both sides of the FT.

Close modal

Different from the cylindrical pipes, the elliptical metal pipes have relatively low stiffness, Thus, the eigen-modes of elliptical pipes have lower frequencies than that of the FT, as shown in Fig. 2. The eigen-frequencies of the first two modes are 933.7 and 1288.2 Hz, lower than that of the first mode of FT (3185.2 Hz). These eigen-modes of elliptical pipe may have negative effects on the LCR transducer driven by Class IV FT. In addition, the low stiffness of the pipes results in the low-frequency and low radiation parameter of the LCR mode.16,17

FIG. 2.

(Color online) Vibration displacement nephograms of the first two flexural modes of the elliptical pipes.

FIG. 2.

(Color online) Vibration displacement nephograms of the first two flexural modes of the elliptical pipes.

Close modal

To analyze the influences of low-stiffness elliptical pipes, finite element models of the LCR transducer, driven by the 33-mode ring, and the Class IV FT are established. A comparison is performed under the following conditions: the two LCR transducers share the same length and the driving source height: the length is 500 mm and the height is 100 mm. The lengths of the front and back pipe are the same. The ratio short-axis–length to long-axis–length is 0.5. The diameter of the piezoelectric ring and the FT shell major-axis length is 200 mm. The thickness of the piezoelectric ring and FT shell is 10 mm. Additionally, the thickness of one piece of piezoelectric ceramic is 5 mm to receive an identical electric field intensity.

The finite element (FE) models of the two LCR transducers are shown in Fig. 3. The FE models of both two LCR transducers are symmetric about the x-y, y-z, and x-z planes. Thus, to accelerate the calculation speed, only one-eighth of the whole FE model has been established and symmetry boundary conditions are applied on the x-y, y-z, and x-z planes. The red regions represent the piezoelectric ceramics; the material is PZT4 (material parameters are shown in the  Appendix). The yellow regions represent the metal pipes, and the gray regions represent the FT shell. The materials of these two parts are all aluminum. The cyan, blue, and purple areas represent the water inside the pipe, the water as acoustic media, and the perfectly matched layer (PML), respectively. The PML absorbs all outgoing wave energy in frequency-domain problems to create a free-field condition. These parts are all water. The brown areas represent the isolation; the material is cork for the transducer with FT driving and polyurethane for the transducer with ring driving. The parameters of these materials are listed in Table I.

FIG. 3.

(Color online) Finite element model of the LCR transducer driven by the (a) 33-mode ring, (b) FT.

FIG. 3.

(Color online) Finite element model of the LCR transducer driven by the (a) 33-mode ring, (b) FT.

Close modal
TABLE I.

Material parameters of structures of the prototype.

Material Density (kg/m3) Young's modulus (Pa) Poisson's ratio
Aluminum  2700  70×109  0.33 
Water  1000     
Steel  7850  200×109  0.30 
Cork  900  0.3×109  0.4 
Polyurethane  1060  0.51×109  0.38 
Material Density (kg/m3) Young's modulus (Pa) Poisson's ratio
Aluminum  2700  70×109  0.33 
Water  1000     
Steel  7850  200×109  0.30 
Cork  900  0.3×109  0.4 
Polyurethane  1060  0.51×109  0.38 

The TVR curves for these two LCR transducers are shown in Fig. 4(a). The solid line represents the TVR of the LCR transducer driven by the FT. There are three resonance peaks in the frequency region below 2000 Hz. From low to high frequency, the first one is the LCR mode, the second one is the flexural mode of the elliptical pipe [shown in Fig. 4(b)], and the third one is the flexural mode of the FT. The TVR value of the LCR mode is approximately 20 dB lower than that of the flexural mode of the FT. On the contrary, the TVR curve of the LCR transducer driven by the 33-mode ring [dashed line in Fig. 4(a)] has two resonance peaks with similar TVR value. In addition, the flexural mode of the elliptical pipe, which is not expected in the transducer, has a negative influence on the coupling between the LCR mode and the flexural mode of the FT. It results in the valley on the TVR curve.

FIG. 4.

(Color online) (a) TVR curves of the LCR transducers driven by the Class IV FT (solid line) and the 33-mode ring (dashed line), (b) the second mode of the LCR transducer driven by the Class IV FT.

FIG. 4.

(Color online) (a) TVR curves of the LCR transducers driven by the Class IV FT (solid line) and the 33-mode ring (dashed line), (b) the second mode of the LCR transducer driven by the Class IV FT.

Close modal
In addition, because fewer piezoelectric ceramics exist in the driving source, the efficiency of LCR mode of an LCR transducer driven by the Class IV FT is expected to be higher. Electroacoustic efficiency is usually used to evaluate a transducer. However, because of the directivity of LCR transducer, the acoustical radiation power is hard to measure. In addition, TVR in acoustic-axis direction is the focus of this paper. The acoustic axis is the minor-axis direction for the transducer with a Class IV FT driving and the radial direction for the transducer with ring driving. Therefore, a parameter η is defined to evaluate the efficiency of the LCR transducer:
η = p far W e ,
(1)
where p far represents the far-field pressure extrapolated back to 1 m in acoustic-axis direction, and W e represents the electric power expended by the piezoelectric ceramics. The physical meaning of parameter η is the pressure produced by a unit of electric power. After calculating η at the frequency of the LCR mode, the LCR transducer driven by the 33-mode ring produces 12.31 Pa/mW electric power. For the LCR transducer with the Class IV FT driving source, the result is 3.93 Pa/mW, which is 68.1% lower.

In summary, it is difficult to achieve multimode LCR transducer by using low-stiffness elliptical pipes. To improve the TVR value and the efficiency of the LCR transducer driven by a Class IV FT, elliptical metal pipes with larger stiffness should be utilized.

Several approaches have been proposed to increase the stiffness of elliptical metal pipes: increasing the thickness, changing the material, or changing the structure. A comparison of the first two methods with the initial model is shown in Fig. 5. The metal pipes using these two approaches have more weight; however, the TVRs of the LCR mode are still not sufficiently high to couple with the flexural mode of the FT. The flexural mode of the metal pipe is still in the region of the LCR and FT flexural modes.

FIG. 5.

(Color online) TVR curves of the LCR transducer with a 10 mm–thick aluminum pipe (solid line), 20 mm–thick aluminum pipe (dashed line), and a 10 mm–thick steel pipe (dotted line).

FIG. 5.

(Color online) TVR curves of the LCR transducer with a 10 mm–thick aluminum pipe (solid line), 20 mm–thick aluminum pipe (dashed line), and a 10 mm–thick steel pipe (dotted line).

Close modal

Consequently, without changing the structure of the FT, an improved aluminum pipe is proposed for the front and back pipe. The improved pipe is still elliptical, and the beam along the minor axis was 10 mm thick, as illustrated in Fig. 6(a). The beam along the minor axis restrains the flexural vibration of the pipe; thus, the stiffness of pipe is improved.

FIG. 6.

(Color online) (a) Structure of improved metal pipe, (b) TVR results of LCR transducer with 10-mm–thick elliptical (dashed line), and 10-mm–thick improved aluminum pipes (solid line).

FIG. 6.

(Color online) (a) Structure of improved metal pipe, (b) TVR results of LCR transducer with 10-mm–thick elliptical (dashed line), and 10-mm–thick improved aluminum pipes (solid line).

Close modal

The improved pipes significantly increase the TVR value and the η parameter of the LCR transducer as shown in Fig. 6(b), and the weight of the pipe does not increase significantly. The TVR value of the LCR mode is close to that of the FT flexural mode and there is no other mode between these two modes. Furthermore, η increase to 13.26 Pa/mW, which is 237% higher than that of the LCR transducer with 10-mm–thick elliptical aluminum pipes and 7.7% higher than the LCR transducer driven by the 33-mode ring. The aims of the multimode LCR transducer driven by the Class IV FT is achieved by using improved elliptical pipes.

The structure of the driving source significantly affects the performance of the entire LCR transducer. A sketch of the Class IV FT is illustrated in Fig. 7. The shape of FT shell is defined by four parameters: the major-axis length (a), the ratio of the minor-axis length to the major-axis length (reciprocal of ellipticity, ratio), the thickness (t), and the height (h). The resonance frequencies and TVR values of the LCR and the FT flexural mode are the performances to evaluate the transducer; the η parameter of the LCR mode is another performance.

FIG. 7.

Illustration of Class IV FT driving source.

FIG. 7.

Illustration of Class IV FT driving source.

Close modal

The target of this study is a more efficient multi-mode LCR transducer prototype compared with a ready-made LCR transducer driven by 33-mode ring. Thus, the LCR transducer driven by Class IV FT has the following preconditions: (1) these two transducers share a similar eigen-frequency (1 kHz), which means the height of the entire transducer is around 400 mm, (2) the same volume of PZT is used in both transducers, so the piezoelectric stack of the FT consists of 26 pieces of PZT4 (70 × 30 × 5 mm). In addition, the target frequency of the FT flexural mode is between 2 and 2.5 kHz, lower than the 3rd order the LCR mode. After meeting the above conditions, the higher the TVR values of both resonance modes and the η of LCR mode, the better.

To study the effect of the length of the FT major axis, all other parameters are maintained constant. The resonance frequency, TVR, and η of the LCR mode are shown in Fig. 8(a). The growth of the major-axis length means the increase in the volume velocity of the FT driving. The TVR value of the LCR transducer should have increased synchronously. However, the resonance frequency of the LCR transducer decreases with the increase in the major-axis length, so the radiation resistance sharply decreases. Thus, under the combined action of the volume velocity and the radiation resistance, the TVR value of the LCR transducer decreases with the growth of the major-axis length. The other parameter, η, is approximately constant because the electric power decreases with the growth of the major-axis length. The resonance frequency and TVR curve of the FT flexural mode is shown in Fig. 8(b); the trends of these two performances are the same as those of the LCR mode. Since the length of major-axis has little influence on the efficiency, the 210 mm major-axis length is chosen to obtain higher TVR value and ensure that the PZT stack can be installed in the FT shell.

FIG. 8.

(Color online) Changes of resonance frequency, TVR, η of LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT major-axis length.

FIG. 8.

(Color online) Changes of resonance frequency, TVR, η of LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT major-axis length.

Close modal

Similarly, while maintaining all other parameters fixed, the ellipticity of the FT is varied. The effects of the ratio variables on the characteristics of the LCR mode are shown in Fig. 9(a). The resonance frequency and η increase linearly with an increase in the ratio, and the TVR also increases. The TVR value grows linearly when the ratio is between 0.5 and 0.6. While the ratio is larger than 0.6, the section of the FT shell is close to a circle rather than an ellipse; thus, the amplitude amplification of the FT shell subsides and the growth rate of the TVR value reduces. In addition, the influences of the ratio to the performances of the FT mode are shown in Fig. 9(b) and the TVR of the FT mode decreases with the growth of the ratio. A higher ratio is beneficial to the LCR mode, but opposite to the FT mode. Finally, 0.6 is chosen in the prototype to balance the TVR values of these two modes.

FIG. 9.

(Color online) Changes of resonance frequency, TVR, η of LCR mode (a) and resonance frequency, TVR the FT mode (b) with respect to the FT ratio.

FIG. 9.

(Color online) Changes of resonance frequency, TVR, η of LCR mode (a) and resonance frequency, TVR the FT mode (b) with respect to the FT ratio.

Close modal

Figure 10(a) shows that the resonance frequency, TVR, and η of the LCR mode change with an increase in the FT thickness with all other parameters fixed. The TVR value and the η increase with the growth of the FT shell thickness because of the increase in the radiation resistance. When the thickness is >15 mm, the decrease in the volume velocity of the FT driving results in the drop of the slope of TVR value. In addition, the FT shell thickness has great influence on the FT flexural mode as Fig. 9(b) shows; the frequency of the FT with an over thick FT shell is higher than the target and the TVR value significantly decreases because of the over high FT shell stiffness. Finally, a 15 mm–thick FT shell is selected in the prototype.

FIG. 10.

(Color online) Changes of resonance frequency, TVR, η of the LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT thickness.

FIG. 10.

(Color online) Changes of resonance frequency, TVR, η of the LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT thickness.

Close modal

For a Class IV FT, a higher shell leads to a larger radiation surface and a lower resonance frequency synchronously as Fig. 11(b) shows. However, for the LCR mode, the radiation surfaces are the up and bottom openings as Fig. 1 shows. Thus, the radiation surfaces stay unchanged with the variation of the FT height. The growth of the FT height increases the volume velocity of the FT driving, but the variation of the frequency leads to the complex variation of the TVR value. The TVR value changes minimally with the variation of the FT height. However, the η parameter significantly decreases with the growth of the FT height. Thus, the 120 mm–high FT shell is selected.

FIG. 11.

(Color online) Changes of resonance frequency, TVR, η of the LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT height.

FIG. 11.

(Color online) Changes of resonance frequency, TVR, η of the LCR mode (a) and resonance frequency, TVR of the FT mode (b) with respect to the FT height.

Close modal

Based on the design target, the multimode LCR transducer prototype driven by the Class IV FT is designed using the structural parameters listed in Table II. The simulation results are shown in Fig. 12. Two resonance peaks exist in the 700–2700 Hz frequency region: the LCR mode at 1030 Hz and the FT flexural mode at 2310 Hz. The TVR values are 134.8 dB (re 1 μPa/V @ 1 m) for the LCR mode and 139.1 dB (re 1 μPa/V @ 1 m) for the flexural mode. The η of the LCR mode is 18.93 Pa/mW, 54% higher than that of the LCR transducer driven by the 33-mode ring (12.31 Pa/mW).

TABLE II.

Structural parameters of the prototype.

Structural parameter Dimension
Total length of transducer  400 mm 
FT major-axis length  210 mm 
Reciprocal of ellipticity  0.6 
FT height  120 mm 
FT thickness  15 mm 
Thickness of metal pipes  15 mm 
PZT stack  70 × 30 × 5 mm3 × 26 pieces 
Structural parameter Dimension
Total length of transducer  400 mm 
FT major-axis length  210 mm 
Reciprocal of ellipticity  0.6 
FT height  120 mm 
FT thickness  15 mm 
Thickness of metal pipes  15 mm 
PZT stack  70 × 30 × 5 mm3 × 26 pieces 
FIG. 12.

TVR curve for prototype of multimode the LCR transducer driven by FT.

FIG. 12.

TVR curve for prototype of multimode the LCR transducer driven by FT.

Close modal

The prototype was fabricated as shown in Fig. 13. The metal pipes were fixed on both sides of the FT shell using steel shanks. The gaps between the pipes and the FT shell were filled with cork mats for isolation. The dimensions of the prototype were 235 × 147 × 406 mm, and its weight was 14.4 kg.

FIG. 13.

(Color online) Prototype multimode LCR transducer driven by FT.

FIG. 13.

(Color online) Prototype multimode LCR transducer driven by FT.

Close modal

The acoustic performance measurements were performed on a ship floating on a vast lake. The distances between the ship and shoresides were over 200 m and the depth of the lake was more than 70 m. The prototype was located at a depth of 30 m which can reduce the echo from the surface and bottom of the lake. An LCR transducer driven by a 33-mode ring. which has similar size and similar resonance frequency of the LCR mode, was measured at the same time (as Fig. 14 shows). The η parameter of these two transducers was the focus of the comparison.

FIG. 14.

(Color online) Scenes of acoustic measurements of the LCR transducer driven by the (a) Class IV FT, (b) 33-mode ring.

FIG. 14.

(Color online) Scenes of acoustic measurements of the LCR transducer driven by the (a) Class IV FT, (b) 33-mode ring.

Close modal

The measurement system consists of the following: a RIGOL DG4062 waveform generator to generate the required burst signal, an Aigtek ATA- 2021H power amplifier to amplify the burst signal and apply it to the transducer, a B&K8105 standard hydrophone placed 1.7 m from the acoustic center of the transducer to receive the acoustic signal and transform it to an electrical signal, a NF3625 programmable filter to amplify and filter the signal received by the hydrophone, and an Agilent DSO-X 3034 A digital oscilloscope to display the processed signal. The signal transmission path and photograph of the measurement equipment are displayed in Fig. 15.

FIG. 15.

(Color online) (a) The transmission path of signal, (b) the composition of the measure system.

FIG. 15.

(Color online) (a) The transmission path of signal, (b) the composition of the measure system.

Close modal

The continuous wave (CW) pulse signal was selected as the transmission signal to weaken the echo from the surface and bottom of the lake. The length of the pulse signal was calculated before measurement. Because the mechanical Q value of the LCR mode was 12, the cycle number of the pulse signal was set to 15, and the trigger interval was set at 1 s. The TVR curve of the prototype and a comparison between the measurement and simulation results are shown in Fig. 16.

FIG. 16.

(Color online) The comparison of the measurement result (solid line) and simulation result (dashed line) of the prototype.

FIG. 16.

(Color online) The comparison of the measurement result (solid line) and simulation result (dashed line) of the prototype.

Close modal

As shown in Fig. 16, the two measurement resonance peaks exist in the 700–2700 Hz frequency band, the same as the simulation. The first resonance peak is the LCR mode, and the second is the flexural mode of the FT. The TVR of the LCR mode is 132.1 dB re 1 μPa/V @ 1 m. which is 2.7 dB lower than that of the simulation result. The LCR resonance frequency is 960 Hz, which is 7.3% lower than that of the simulation. The TVR of the flexural mode is 137.8 dB re 1μPa/V @ 1 m, which is 1.3 dB lower than that of the simulation. The resonance frequency of the flexural mode is 2150 Hz, which is 7.4% lower than that of the simulation. The η of the LCR mode was 14.13 Pa/mW, which is 25% lower than that of the simulation.

The measured results are in good agreement with the simulation results, particularly for the flexural mode. The manufacturing processes, such as the method to apply prestress on the PZT stack and the material of the isolation, are relatively mature; thus, the error is relatively smaller. For the LCR mode, the effects of the additional structures, such as the steel shanks, are ignored in the simulation. Additionally, there is turbulent flow under the surface of the lake; the relative position of the standard hydrophone and the acoustic source may change underwater. Because of the directionality of the LCR transducer, the deviation of the standard hydrophone from the acoustic axis may lead to the error of the measurement. Another reason for the error is that the material parameters of isolation are uncertain because the simulation are estimated values.

As a comparison, the TVR and η parameter of the LCR mode for the transducer driven by a 33-mode ring is 142.7 dB re 1 μPa/V @ 1 m and 10.92 Pa/mW, respectively. The TVR value of the transducer with Class IV FT driving is relatively lower than that of the transducer with a 33-mode ring. However, the η parameter of the transducer with the 33-mode ring is 10.92 Pa/mW, the η parameter of the transducer with FT driving is 14.13 Pa/mW, 29.4% higher. Therefore, the LCR transducer driven by the Class IV FT is a more efficient LCR transducer than the LCR transducer driven by the 33-mode ring.

An LCR transducer driven by a Class IV FT is a new LCR transducer design. Despite utilizing a longitudinal LCR mode identical to that of a LCR transducer driven by a 33-mode ring, the low-stiffness elliptical pipes of the LCR transducer driven by the FT performed poorly. An improved elliptical pipe with a beam along the minor-axis is proposed and used in the LCR transducer driven by a Class IV FT. The multimode LCR transducer driven by a Class IV FT that couples the LCR mode and the flexural mode of the FT is achieved. Through the optimal design of the FT, the multimode prototype has two resonance peaks in the 700–2700 Hz region: the LCR mode at 950 Hz and the FT flexural mode at 2130 Hz. The TVRs of the two peaks are 132.1 dB re 1 μPa/V @ 1 m and 137.8 dB re 1 μPa/V @ 1 m, respectively. The η of the LCR mode peak is 14.13 Pa/mW, 29.4% higher than the LCR transducer driven by the 33-mode ring. The LCR transducer driven by a Class IV FT is a low-frequency, deep-water, high-efficiency, broadband underwater transducer with great potential.

The material parameters of PZT4 used in finite element simulation is as follows:

The density is 7500 kg/m3.

The matrix of elastic compliance coefficients is
s E = [ 1.23 × 10 11 4.05 × 10 12 5.31 × 10 12 0 0 0 4.05 × 10 12 1.23 × 10 11 5.31 × 10 12 0 0 0 5.31 × 10 12 5.31 × 10 12 1.55 × 10 11 0 0 0 0 0 0 3.9 × 10 11 0 0 0 0 0 0 3.9 × 10 11 0 0 0 0 0 0 3.27 × 10 11 ] ( 1 / Pa ) .
The matrix of piezoelectric coefficients is
d = [ 0 0 0 0 4.96 × 10 10 0 0 0 0 4.96 × 10 10 0 0 1.23 × 10 10 1.23 × 10 10 2.89 × 10 10 0 0 0 ] ( C / N ) .
The matrix of relative dielectric constant is
ε T = [ 1475 0 0 0 1475 0 0 0 1300 ] .
1.
R.
Spindel
,
R.
Porter
, and
D.
Webb
, “
A mobile coherent low-frequency acoustic range
,”
IEEE J. Ocean. Eng.
2
(
4
),
331
337
(
1977
).
2.
P.
Worcester
,
R.
Spindel
, and
B.
Howe
, “
Reciprocal acoustic transmissions: Instrumentation for Mesoscale monitoring of ocean currents
,”
IEEE J. Ocean. Eng.
10
(
2
),
123
137
(
1985
).
3.
C.
Gac
,
Y. L.
Gall
,
T.
Terre
,
B.
Leduc
, and
R.
Person
, “
A new modular instrumentation for ocean acoustic tomography, present status and future trends
,” in
IEEE Oceanic Engineering Society. OCEANS'98. (Cat. No.98CH36259)
(
1998
), pp.
1219
1223
.
4.
A. K.
Morozov
, “
Tunable and broadband resonator pipe sound sources for ocean acoustic tomography, communications and long-range navigation
,” in
OCEANS 2017 - Aberdeen
, Aberdeen (
2017
), pp.
1
8
.
5.
T.
Marsset
,
B.
Marsset
,
S.
Ker
,
Y.
Thomas
, and
Y.
Le Gall
, “
High and very high resolution deep-towed seismic system: Performance and examples from deep water Geohazard studies
,”
Deep Sea Res. Part I Oceanogr. Res. Pap.
57
(
4
),
628
637
(
2010
).
6.
S.
Ker
,
B.
Marsset
,
S.
Garziglia
,
Y.
Le Gonidec
,
D.
Gibert
,
M.
Voisset
, and
J.
Adamy
, “
High-resolution seismic imaging in deep sea from a joint deep-towed/OBH reflection experiment: Application to a mass transport complex offshore Nigeria
,”
Geophys. J. Int.
182
(
3
),
1524
1542
(
2010
).
7.
T. F.
Duda
,
S. M.
Flatté
, and
J. A.
Colosi
, “
Measured wave‐front fluctuations in 1000‐km pulse propagation in the Pacific Ocean
,”
J. Acoust. Soc. Am.
92
(
2
),
939
955
(
1992
).
8.
J. B.
Lee
, “
Low-frequency resonant-true projector for underwater sound
,” in
Ocean'74-IEEE International Conference on Engineering in the Ocean Environment
(
1974
), pp. 10–15.
9.
D. C.
Webb
,
A. K.
Morozov
, and
T. H.
Ensign
, “
A new approach to low frequency wide-band projector design
,” in
Oceans '02 MTS/IEEE
(
2002
), pp.
2342
2349
.
10.
A. K.
Morozov
, “
Underwater ultra-low frequency seismic source
,”
J. Acoust. Soc. Am.
149
(
4
),
2163
2172
(
2021
).
11.
A. K.
Morozov
and
D. C.
Webb
, “
Underwater infra-sound resonator for long range acoustic and seismic survey
,” in
Proceedings of OCEANS'19—Marseille
, Marseille, France (June 17–20,
2019
).
12.
J.-N.
Decarpigny
,
B.
Hamonic
, and
O. B.
Wilson
, “
The design of low frequency underwater acoustic projectors: Present status and future trends
,”
IEEE J. Ocean. Eng.
16
(
1
),
107
122
(
1991
).
13.
B.
Ji
,
L.
Hong
, and
Y.
Lan
, “
Influences of length and position of drive-stacks on the transmitting-voltage-response of the broadband Tonpilz transducer
,”
J. Acoust. Soc. Am.
150
(
6
),
4140
4150
(
2021
).
14.
G.
Brigham
and
B.
Glass
, “
Present status in flextensional transducer technology
,”
J. Acoust. Soc. Am.
68
,
1046
1052
(
1980
).
15.
K. P. B.
Moosad
,
G.
Chandrashekar
,
M. J.
Joseph
, and
R.
John
, “
Class IV flextensional transducer with a reflector
,”
Appl. Acoust.
72
(
2–3
),
127
131
(
2011
).
16.
G. W.
McMahon
, “
Performance of open ferroelectric ceramic cylinders in underwater transducers
,”
J. Acoust. Soc. Am.
36
,
528
533
(
1964
).
17.
Y.
Sang
,
Y.
Lan
, and
Y.
Ding
, “
Study on elastic-wall fluid cavity resonant frequency of Helmholtz underwater acoustic transducer
,”
Acta Phys. Sin.
65
(
2
),
024301
(
2016
).