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Analysis of Acoustic Characteristics of Piezoelectric Underwater Acoustic Transducer

Views: 0     Author: Site Editor     Publish Time: 2021-10-14      Origin: Site

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Thepiezoelectric underwater acoustic transduceris an underwater detection device that can work as both a driver and a sensor. Accurate prediction of its acoustic characteristics in a noisy underwater environment is very important for the design of a robust and durable transducer. The finite element method is very effective and practical for analyzing the various performances of the transducer in different environments. A two-dimensional axisymmetric finite element model of a Tonpilz-type transducer was established, a program based on the finite element method was designed, and dynamic analysis was performed on it, including modal analysis and harmonic response analysis, etc., and some acoustic characteristics were obtained. The results of the program analysis and the ANSYS software analysis results show a good agreement.

 

 

1 Introduction

Hydroacoustic transducers play a key role in hydroacoustic engineering. In recent years, with the rapid development of science and technology, the continuous development of new transducer materials and the application of new analysis methods in the design of transducers have made the transducer Many new concepts and new methods have emerged in the research and design of. As a kind of smart material, piezoelectric materials are widely used in electromechanical fields, such as piezoelectric ceramic transformers and sonar transducers. Thepiezoelectric hydrophone transducer is an underwater detection device, which can work as a driver or a sensor. In most underwater detection applications, piezoelectric transducers show good overall performance: high work efficiency, flexible design, and high cost performance. Accurately pre-calculating its acoustic parameters in a noisy underwater environment is very important for the design of a robust and durable transducer. The finite element method (abbreviated as FEM) can be widely used in engineering analysis. It can analyze the performance of the transducer in different environments (such as in the air or in the water). a two-dimensional axisymmetric finite element model of a Tonpilz-type transducer is established, which can perform modal, underwater harmonic response and admittance analysis. The analysis tool uses an underwater sensor analysis program based on the finite element method (USAP for short). This program is very practical for analyzing the parameters of the transducer working in the water, as long as the necessary input files are prepared and the analysis type is selected, the corresponding analysis can be made.

 

2 Theoretical analysis

 

2.1 Description of the working environment of the transducer in the water

Figure 1 shows the working environment of the transducer in water. The transducer can be represented by a combination of elastic and smart materials. A limited water area is included around the transducer, and different boundaries and working conditions are considered. An infinite fluid boundary is set at the outermost periphery of the limited water area to make it closer to the real working state. Therefore, the theoretical analysis involved includes the coupling between fluid and solid structure and the coupling between electricity and structure in piezoelectric materials.

 

2.2 Finite element analysis of fluid-solid coupling field

The harmonic response analysis of a solid structure in a fluid environment must involve the interaction between the solid structure and the fluid. Assuming that the solid structure is an elastic body, its behavior characteristics conform to the theory of elasticity. Assuming that the fluid is compressible (that is, the density changes with pressure changes), non-viscous (that is, there is no viscous dissipation) and non-flowable medium, and its average density and pressure remain uniform in the analyzed watershed, then meet the corresponding wave equation. For the finite element analysis of the solid structure, this equation considers the pressure load of the fluid applied to the solid structure interface at the fluid-solid interface.Where U is the nodal displacement; P is the nodal fluid pressure; M is the mass matrix of the structure; C is the damping matrix of the structure; K is the stiffness matrix of the structure; Q is the coupling area matrix on the fluid-solid interface; f is the solid structure The force vector on the top. For fluid finite element analysis, based on the variational principle or the weighted residual method (ie Galerkin method), the wave equation can be discretized by standard finite element, and finally the fluid finite element control equation can be obtained. This equation takes into account the continuity requirements on the fluid-solid interface and the energy loss due to damping. Where E is the moment of inertia of the fluid matrix; A is the damping matrix of the fluid; H is the stiffness matrix of the fluid; ρ is the density of the fluid; the upper right index T is the transpose of the matrix. Equations (1) and (2) give the fluid-solid coupling equations, which can be combined as follows: f1 is the structural force vector acting on the fluid-solid interface; f2 is caused by the initial wave force (wave force) field The force vector acting on the fluid-solid interface. Since the displacement can be regarded as the gradient of the velocity potential, another expression form of the fluid-solid finite element coupling equation corresponding to the equation (3) can be obtained through equation (4).

 

2.3 Finite element analysis of electric-structure coupling field

Piezoelectric hydroacoustic transducers use piezoelectric materials, so it is important to understand how it works. Based on the quasi-static assumption, that is, the electric field must be balanced with the elastic displacement field, the linear constitutive equation for piezoelectric materials can be obtained. T is the stress field; D is the electric displacement; S is the strain field; EV is the electric field; e is the pressure Electrical coupling constant matrix; εS is the dielectric constant matrix; cE is the elastic stiffness matrix of the piezoelectric material. Is the damping matrix of piezoelectric materials; KUΦ is the piezoelectric coupling matrix; KΦΦ is the dielectric stiffness matrix; F is the total applied force vector; G is the total applied charge.

 

3 Finite element modeling and analysis

3.1 Finite element model of Tonpilz type transducer

Figure 2 shows the physical schematic diagram of the Tonpilz transducer, which consists of four parts: head, tail, tension bolt and piezoelectric ceramics. Two pieces of piezoelectric ceramics are sandwiched between the head and the tail, and a tension bolt is placed in the center to ensure close contact between the various parts. The transducer head is cylindrical, so it has a circular radiating surface. Studies have shown that the geometric parameters of each part of the transducer have a direct impact on its mechanical quality factors, which can be optimized by some methods]. The detailed dimensions and specific material parameters of each component of the transducer in this article are shown separately.

 

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Table 1 and Table 2. Figure 3 shows the two-dimensional axisymmetric finite element model and boundary conditions of the Tonpilz transducer. The model is established on the X-Y plane, and its symmetry axis is along the X axis. The finite element model uses four-node quadrilateral axisymmetric elements for meshing, including 193 elements and 240 nodes. The two piezoelectric underwater acousticsare placed in opposite polarities, and the polarization direction is along the longitudinal direction of the transducer, which can improve the response performance of the transducer. Three electrodes are placed on the contact surface related to piezoelectric ceramics for excitation or measurement. The Y-direction restricts the outer cylindrical surface of the head, and the X-direction restricts the peripheral end surface of the head close to the piezoelectric ceramic but not in contact with the electrode. This restriction reflects the consideration of the actual boundary conditions of the transducer Fixed for the head. The force direction of the transducer is the X direction. When it works, it will vibrate in this direction.

 

3.2 Modal analysis of Tonpilz transducer

Table 3 lists the first 5 natural frequencies obtained from the modal analysis of the Tonpilz transducer in the short-circuit state, and compares the analysis results of USAP and ANSYS. Figure 4 shows the comparison of the first three natural frequency modes. It can be seen that the analysis results of USAP and ANSYS are in good agreement.

 

3.3 Harmonic response analysis of Tonpilz-type transducer in water

Figure 5 shows the two-dimensional axisymmetric model of the Tonpilz transducer in water, which is also divided by 4-node quadrilateral axisymmetric elements, with 383 elements and 444 nodes. The specific structure and boundary conditions of the Tonpilz transducer are the same as those shown in Figure 3. In the model in Figure 5, the head of the Tonpilz transducer is in contact with the front face of the tension bolt and water. When performing harmonic response analysis, a sinusoidal voltage with an amplitude of 1V is set on the middle electrode, and the other two electrodes are at a voltage of 0V. The frequency range of the analysis is set to 10000Hz~ 50000Hz. Through the harmonic response analysis, the Tonpilz-type transducer emits voltage response (TVR for short) and pressure analysis results in water as shown in Figure 6. Node 419 is selected as the calculation point to be analyzed. Analyze Figure 6 to get

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Its first-order resonance frequency is around 19045Hz. At this frequency, the pressure distribution in the water and the deformation of the Tonpilz transducer are shown in the figure.

 

Admittance analysis of Tonpilz type transducer in water

 

Admittance or impedance is also an important characteristic parameter of the transducer. It is a function of the mechanical and acoustic characteristics of the transducer, and is an effective method for analyzing and studying the performance of the transducer . After analysis, the admittance here is a complex number, expressed in the following form:During analysis, set a voltage of 1V on the middle electrode, and a voltage of 0V on the remaining two electrodes. After calculation, the analysis results of the conductance and susceptance of the Tonpilz-type transducer in water are shown in Figure 8. Both conductance and susceptance have peaks at the resonance frequency.

 

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4 Conclusion

The finite element method is very effective and practical for analyzing the acoustic parameters of piezoelectric acoustic transducers. The axisymmetric finite element model of the Tonpilz type transducer established in this paper is analyzed by the USAP program for dynamics (including harmonic response and modal, etc.). The results obtained reasonably describe the acoustic parameters of this type of underwater acoustic transducer. There are still some shortcomings in the establishment and analysis of the model, which need to be further improved and perfected.

 

 



 

 

 


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