Research on Volume Array Based on Curved Disk Transducers

A curved disk transducer with a dual stack structure with a resonant frequency of 800Hz is used as the array element, and the mutual radiation effect between the transducer elements is utilized to form a densely arranged volume array. Based on the formation structure, establish corresponding finite element models in COMSOL software to simulate and analyse the acoustic performance of different volume arrays. Finally, prototype production and array acoustic performance testing were conducted, and the measured data basically matched the simulation results. The results show that compared to a single transducer, utilizing the mutual radiation effect between the transducer elements can effectively reduce the resonant frequency of the volumetric array and expand its operating bandwidth, while also improving the maximum sound source level after formation. In addition, with a reasonable number of array elements, keeping the spacing between the elements constant, the more elements there are, the lower the resonant frequency of the volumetric array, the smaller the quality factor, and the higher the emission voltage response.


Introduction
In traditional transducer arrays, in order to avoid the impact of mutual radiation on the overall performance of the array, it is always advisable to ensure that the spacing between the array elements is not less than 2  .Even in order to increase power capacity and achieve better directionality, efforts will be made to avoid spacing between array elements less than 4  .The conventional array formation method is to combine the transducer elements in the height direction into a linear array, utilizing the mutual radiation effect of the transducer elements to reduce resonance frequency and achieve lowfrequency and high-power radiation.This is also the focus of current research by scholars, and there is relatively little research on expanding the distribution into a matrix in the horizontal direction.This article adds a distribution combination in the horizontal direction on the basis of the height direction array, establishes a densely arranged volume array, and conducts research and analysis on the resonance frequency, operating bandwidth, and transmission voltage response of different formation volume arrays.
By closely arranging the array in a small size and utilizing the strong mutual radiation effect between the array elements, the aim is to reduce the resonant frequency, expand the working bandwidth, and improve the emission ability after the array is formed [1][2][3].The theoretical calculation of the mutual radiation effect under dense arrangement is very complex, and finite element software is generally used to simulate and analyse the performance of the entire array.Each element transducer of a linear array (half wavelength) is an independent individual, and when establishing a finite element model, the model can be simplified as much as possible to improve computational speed.The performance of the entire array is determined by the comprehensive action of each array element transducer.Only by accurately calculating the impedance and vibration characteristics of all array element transducers can the mutual radiation effect be quantitatively analysed.Finally, prototype production and array testing were conducted, and the simulation analysis was in good agreement with the measured results.

Comparison between Simulation and Measurement of Array Element Bending Disk
The array element bending disk structure used in this article is a classic double layered structure with an air cavity.Piezoelectric circular plates with opposite thickness polarization directions are bonded to the upper and lower sides of the metal support plate, and the circuit is connected in series to form edge simple support conditions.When an electrical signal is applied, the thickness vibration of the ceramic disc drives the support plate to bend and vibrate, radiating sound waves symmetrically on both sides.Its modelling in the fluid is shown in Figure 1 [4].
After watertight sealing of the oscillator, a single element transducer weighs approximately 2 kg.Conduct acoustic performance testing, and the comparison between the measured results and the simulated transmission voltage response level curve is shown in Figure 2. The resonance frequency of the array element in the figure is 800Hz, with a response of 130.5 dB and a response bandwidth of 12.5% at -3 dB The measured results are in good agreement with the simulation results.
In the formula, dmn is the distance between the m-th and n-th array element transducers, and k is the wavenumber, ρ C is the dielectric impedance, and S0 is the radiation area of the array element transducer.The real part is the mutual radiation resistance coefficient, and the imaginary part is the mutual radiation impedance coefficient.From the equation, it can be seen that the mutual radiation impedance coefficient between the m-th and n-th array element transducers is related to the radiation area of the array element transducer, the distance between the array elements, the position of the array elements, and the sound field medium.Therefore, the radiation area of the transducer, the spacing between array elements, the position of array elements, and the sound field medium are all factors that affect the mutual radiation effect.

Comparison between Simulation and Measurement of Different Formation Volume Arrays
Use simulation software to establish a finite element model of densely arranged volume arrays and simulate and analyse the electro-acoustic characteristics of different formations of densely arranged volume arrays.Using a curved disk with a resonant frequency of f0 as the array element for array design, MPS-3 can be assembled × 1. MPS 3 × 4 and MPS-3 × 8, including MPS-3 × 8 is composed of 3 sets of densely arranged linear arrays with a horizontal spacing of 216 mm and an equilateral triangle distribution.Each set of densely arranged linear arrays consists of 8 curved disk transducers arranged with a vertical spacing of 12 mm, consisting of a total of 24 curved disk transducers.Its modeling is shown in Figure 3.

Figure 3. MPS-3 X 8 Volume Matrix Modeling
In order to better and more accurately obtain waveforms and avoid the superposition of reflected waves, the main method is the reflection superposition from the lake surface, with a depth of 30 meters and a horizontal spacing of 1.5 meters.The measured data of different formations are shown in Figure 4, and the performance parameter comparison is shown in Table 1.When the spacing between the array elements remains constant, the higher the number of array elements, the lower the resonant frequency of the array, the smaller the quality factor, and the higher the emission voltage response.
However, as the number of array elements changes, the overall performance of the array does not necessarily change linearly in a certain direction.As the number of array elements increases, the mutual radiation effect between the elements becomes greater.When the mutual radiation effect is equivalent to or even greater than the self-radiation impedance of the transducer, the vibration mode of the transducer will change, and the impedance and electro-acoustic efficiency of the transducer will also change, resulting in changes in the overall performance of the array.Therefore, as the number of array elements increases, the efficiency of the transducer and the entire array decreases, this in turn affects the voltage response of the entire array.Compare the measured data and simulation results of MPS-3X8, and conduct maximum sound source level testing, as shown in Figures 5 and 6.

Conclusion
This article compares the simulation calculation with the test results of the actual prototype production.
It can be concluded that the bending disc transducer can be utilized to form a small-scale dense array, which can obtain a small-scale low-frequency sound source by utilizing its small size, low frequency, and regular appearance.By using different array distribution methods (vertical and horizontal), volume arrays with different resonant frequencies, bandwidths, and emission capabilities can be obtained, facilitating modular production of products and meeting the performance requirements of different products.

Figure 1 .
Figure 1.Model diagram of the bent disk of the array element

Figure 2 .
Figure 2. Comparison between Actual Measurement and Simulation Results of Array Element Bending Disk

Figure 4 .
Figure 4. Measured data of different formations

Figure 5 .Figure 6 .
Figure 5.Comparison between Actual Measurement and Simulation Results of MPS-3X8

Table 1 .
Measured data of different formations.By comparing the measured results of volume arrays of different formations, it can be seen that the resonant frequency of densely arranged volume arrays is much lower than that of a single transducer;