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The vibro-acoustic analysis of a matching layer attached on a 1–3 piezoelectric composite transducer

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Abstract

A well-designed matching layer attached to a transducer is an effective method to obtain broad bandwidth. In practical applications, the optimal material parameters and geometric parameters for the matching layer are required to be calculated precisely. In this paper, we propose a fluid–structure interaction model for vibro-acoustic analysis of the transducer. An analytical solution to determine the electrical impedance of a transducer with a matching layer immersed in water is derived. The influence of matching layer on the performance of the transducer is demonstrated clearly. To verify the proposed model, a 1–3 piezoelectric composite transducer with a matching layer according to the our proposed model is fabricated. Consequently, the theoretical model we proposed can accurately predict the electrical impedance of the transducer with a matching layer. According to the model, the optimal thickness and acoustic impedance for the matching layer to expand the conductance bandwidth of the transducer can be figured out accurately. In addition, our proposed model also provides a reference for designing a transducer with a matching layer.

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All data generated or analysed during this study are included.

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Abbreviations

\(c_{33}^{E}\) :

Elastic stiffness constant \({N \mathord{\left/ {\vphantom {N {m^{2} }}} \right. \kern-\nulldelimiterspace} {m^{2} }}\)

\(\varepsilon_{33}^{E}\) :

 Dielectric constant \({F \mathord{\left/ {\vphantom {F m}} \right. \kern-\nulldelimiterspace} m}\)

\({\text{e}}_{33}\) :

Piezoelectric stress constant \({C \mathord{\left/ {\vphantom {C {m^{2} }}} \right. \kern-\nulldelimiterspace} {m^{2} }}\)

\(\rho^{c}\) :

Piezoelectric phase density \({{Kg} \mathord{\left/ {\vphantom {{Kg} {m^{3} }}} \right. \kern-\nulldelimiterspace} {m^{3} }}\)

\(\rho^{p}\) :

Aggregate phase density \({{Kg} \mathord{\left/ {\vphantom {{Kg} {m^{3} }}} \right. \kern-\nulldelimiterspace} {m^{3} }}\)

\(u_{i}\) :

Displacement vector \(m\)

\(T_{ij}\) :

Stress tensor \({N \mathord{\left/ {\vphantom {N {m^{2} }}} \right. \kern-\nulldelimiterspace} {m^{2} }}\)

\(S_{ij}\) :

Strain tensor

\(E_{i}\) :

Electric field vector \({V \mathord{\left/ {\vphantom {V m}} \right. \kern-\nulldelimiterspace} m}\)

\(D_{i}\) :

Electric displacement vector \({C \mathord{\left/ {\vphantom {C m}} \right. \kern-\nulldelimiterspace} m}^{2}\)

\(\phi\) :

Electric potential \(V\)

\(c_{ijkl,} c_{pq}\) :

Elastic constant \({N \mathord{\left/ {\vphantom {N m}} \right. \kern-\nulldelimiterspace} m}^{2}\)

\(e_{kij}\) :

Piezoelectric constant \({C \mathord{\left/ {\vphantom {C m}} \right. \kern-\nulldelimiterspace} m}^{2}\)

\(\varepsilon_{ik}\) :

Dielectric constant \({F \mathord{\left/ {\vphantom {F m}} \right. \kern-\nulldelimiterspace} m}\)

\(\rho\) :

Piezoelectric vibrator density \({{Kg} \mathord{\left/ {\vphantom {{Kg} m}} \right. \kern-\nulldelimiterspace} m}^{3}\)

\(p\) :

Pressure amplitude of Ultrasonic wave \(Pa\)

\(\omega\) :

Angular frequency (2πf)\(Hz\)

\(k\) :

Wave number \(m^{ - 1}\)

\(c\) :

Speed of ultrasound \({m \mathord{\left/ {\vphantom {m s}} \right. \kern-\nulldelimiterspace} s}\)

\(Z\) :

Electrical impedance \(\Omega\)

\(S\) :

Electrode surface area \(m^{2}\)

\(d\) :

Diameter of the 1–3 Piezoelectric composite disc \(m\)

\(h\) :

Thickness of the 1–3 Piezoelectric composite disc \(m\)

\(k_{33}\) :

Thickness-extensional Coupling factor

\(V\) :

 Voltage \(V\)

\(I\) :

Electric current \(A\)

\(Y\) :

Admittance \(S\)

\(G\) :

Conductance \(S\)

\(B\) :

Susceptance \(S\)

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Acknowledgements

This work was supported by the Natural Science Foundation Project of Chongqing under Grant cstc2019jcyj-msxmX0098.

Funding

This work was supported by the Natural Science Foundation Project of Chongqing under Grant cstc2019jcyj-msxmX0098.

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Author notes

  1. Yi Liu and Yingqi Sun are shared first authors and contributed equally to the article.

Authors and Affiliations

  1. State Key Laboratory of Ultrasound in Medicine and Engineering, College of Biomedical Engineering, Chongqing Key Laboratory of Biomedical Engineering, Chongqing Medical University, Chongqing, 400016, China

    Yi Liu, Yingqi Sun, Yang Wang, Deping Zeng & Zengtao Yang

  2. School of Science and Engineering, University of Dundee, Dundee, DD1 4HN, UK

    Zhihong Huang

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  1. Yi Liu
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  2. Yingqi Sun
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  3. Zhihong Huang
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  4. Yang Wang
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  5. Deping Zeng
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  6. Zengtao Yang
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Contributions

Concepts and ideas: ZTY and DPZ; Experimental design: YQS and YL; Collect and assemble data: YL and YW; Data analysis and interpretation: all authors; Manuscript writing: all authors; Final approval of the manuscript: all authors; Responsible for all aspects of the work: all authors.

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Correspondence to Deping Zeng or Zengtao Yang.

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Liu, Y., Sun, Y., Huang, Z. et al. The vibro-acoustic analysis of a matching layer attached on a 1–3 piezoelectric composite transducer. J Electroceram 48, 102–109 (2022). https://doi.org/10.1007/s10832-022-00277-8

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  • DOI: https://doi.org/10.1007/s10832-022-00277-8

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