# Piezoelectric Composite Vibrator with a Bilaminated Structure for Bending Vibration

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## Abstract

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## Featured Application

**The 2-2 piezoelectric composite bilaminated vibrator with lower resonance frequency and larger vibration displacement used for making low frequency acoustic transducer.**

## Abstract

## 1. Introduction

_{h}and g

_{h}of high hydrostatic pressure. In underwater acoustic applications, the hydrostatic piezoelectric constant d

_{h}= d

_{33}+ 2d

_{31}of ordinary PZT. Because d

_{33}is approximately equal to −2d

_{31}, d

_{h}is very small. In piezoelectric composites, d

_{31}is reduced by controlling the volume fraction of PZT phase, thus d

_{h}is increased. The dielectric constant of piezoelectric composites is very small, which makes g

_{h}= d

_{h}/ε much larger than that of ordinary PZT. Therefore, piezoelectric composite materials are ideal materials for hydrophones. (5) Smaller plane electromechanical coupling coefficient. In piezoelectric composites, PZT columns are coupled by polymers, and the plane electromechanical coupling coefficient of PZT columns is smaller than that of ordinary PZT columns. Therefore, the radial mode in piezoelectric composites is weaker than that in ordinary PZT, which makes the energy more concentrated on the thickness mode, which improves the time response of the pulse to a certain extent. (6) Flexible polymers, such as epoxy resins, are more flexible at high temperatures, which can make piezoelectric composites into some specific shapes to meet the special requirements of practical applications. In the past, in the fabrication of focusing transducers, acoustic lenses were added to the surface of PZT or piezoelectric single crystal to narrow or focus the sound beam at a certain point in space. Using piezoelectric composites, spherical or cylindrical concave surfaces with certain curvature can be pressed at high temperatures, so that sound waves can be directly focused at the center of curvature, generating point or line focused beams, thus avoiding the trouble of making sound lenses and calculating the location of focus. At the same time, it can reduce the loss caused by the acoustic lens and improve the sensitivity of the transducer. In the present work, piezoelectric composite materials were used to replace piezoelectric ceramics to fabricate a bilaminated vibrator, improve the vibration displacement, and reduce the resonance frequency.

## 2. Structure of the Bilaminated Piezoelectric Composite Vibrator

## 3. Finite Element Simulation of the Piezoelectric Composite Bilaminated Vibrator

_{s}and f

_{p}refer to the series resonance frequency and the parallel resonance frequency, respectively. The results are listed in Table 2.

^{−11}m, and that of the 1-3 vibrator was 3.72 × 10

^{−11}m, where the driving voltage was 1 V. Moreover, the maximum vibration displacement of the 2-2 vibrator was twice greater than that of the 1-3 vibrator, suggesting that the 2-2 composite is superior to the 1-3 composite in the preparation of the piezoelectric composite bilaminated vibrator.

## 4. Fabrication and Performance Test of the Bilaminated Vibrator

_{s}(the frequency corresponding to the maximum admittance mode) and the parallel resonance frequency f

_{p}(the frequency corresponding to the maximum impedance mode). The bandwidth was also read. The parameters of the five groups of 2-2 piezoelectric composite bilaminated vibrator samples were measured via the above test method. The results are shown in Table 3. The electromechanical coupling coefficients of the 2-2 piezoelectric composite bilaminated vibrator listed in Table 3 were calculated using Equation (1).

_{s}, parallel resonance frequency f

_{p}, bandwidth B, electromechanical coupling coefficient, and maximum vibration displacement are listed in Table 4.

_{33}of the material. However, the theoretical parameters used in ANSYS simulation calculation in this paper have errors with the actual material parameters, which need to be further studied. However, the ANSYS calculation results of vibration displacement of 2-2 type piezoelectric composite bi-laminate vibrator basically coincide with the actual test results. The reason is that the piezoelectric strain constant of bi-laminate oscillator increases rapidly with the addition of polymer phase. The strain of composite bi-laminate vibrator is mainly determined by Young’s modulus and volume percentage of polymer phase. Therefore, the piezoelectric strain constant d

_{33}has little effect on the corresponding variables of the PZT ceramic column under the same electric field strength.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Schematic of the series and parallel arrangements of the piezoelectric layers. (

**a**) Parallel arrangement. (

**b**) Series arrangement.

**Figure 4.**Finite element models of the 2-2 and 1-3 piezoelectric composite bilaminated vibrators. (

**a**) 2-2. (

**b**) 1-3.

**Figure 6.**Displacement deformation graph of the 2-2 and 1-3 piezoelectric composite bilaminated vibrators. (

**a**) 2-2. (

**b**) 1-3.

**Figure 7.**Vibration displacement curves of the 2-2 and 1-3 type piezoelectric composite bilaminated vibrators.

**Figure 10.**(

**a**) Admittance curves of the 2-2 piezoelectric composite bilaminated vibrator and the ceramic vibrator. (

**b**) Vibration displacement curves of the 2-2 piezoelectric composite bilaminated vibrator and the ceramic vibrator.

**Figure 17.**(

**a**) Admittance curves of the 2-2 and ceramic vibrators. (

**b**) Vibration displacement curves of the 2-2 and ceramic vibrators.

Parameters | PZT-5A | Parameters | Epoxy Resins |
---|---|---|---|

$\rho $ (kg/m^{3}) | 7750 | $\rho $ (kg/m^{3}) | 1050 |

${c}_{11}^{E}$ (10^{10}N/m^{2}) | 12.1 | ${c}_{11}^{E}$ (10^{10}N/m^{2}) | 0.36 |

${c}_{12}^{E}$ (10^{10}N/m^{2}) | 7.54 | ${c}_{12}^{E}$ (10^{10}N/m^{2}) | 0.138 |

${c}_{13}^{E}$ (10^{10}N/m^{2}) | 7.52 | ${s}_{11}^{E}$ (10^{−12}m^{2}/N) | 278 |

${c}_{33}^{E}$ (10^{10}N/m^{2}) | 11.1 | ${s}_{12}^{E}$ (10^{−12}m^{2}/N) | −97 |

${s}_{11}^{E}$ (10^{−12}m^{2}/N) | 16.4 | ${\epsilon}_{33}^{S}/{\epsilon}_{0}$ | 4 |

${s}_{12}^{E}$ (10^{−12}m^{2}/N) | −5.74 | ${\epsilon}_{33}^{T}/{\epsilon}_{0}$ | 4 |

${s}_{13}^{E}$ (10^{−12}m^{2}/N) | −7.22 | ||

${s}_{33}^{E}$ (10^{−12}m^{2}/N) | 18.8 | ||

d_{31} (10^{−12}C/N) | 470 | ||

d_{33} (10^{−12}C/N) | −171 | ||

e_{31} (C/m^{2}) | −5.4 | ||

e_{33} (C/m^{2}) | 15.8 | ||

${\epsilon}_{33}^{S}/{\epsilon}_{0}$ | 830 | ||

${\epsilon}_{33}^{T}/{\epsilon}_{0}$ | 1700 |

Type | Series Resonance Frequency f_{s} (Hz) | Parallel Resonance Frequency f_{p} (Hz) | Bandwidth (Hz) | Electromechanical Coupling Coefficient |
---|---|---|---|---|

2-2 type | 4630 | 4850 | 760 | 0.298 |

1-3 type | 6075 | 6325 | 420 | 0.278 |

Number of Vibrators | Series Resonance Frequency/f_{s} (Hz) | Parallel Resonance Frequency/f_{p} (Hz) | Electromechanical Coupling Coefficient/k_{e} | Maximum Displacement/S_{m} (10^{−11} m) |
---|---|---|---|---|

1 | 4628 | 4848 | 0.2978 | 7.81 |

2 | 4630 | 4850 | 0.2978 | 7.79 |

3 | 4628 | 4850 | 0.2978 | 7.82 |

4 | 4630 | 4850 | 0.2978 | 7.79 |

5 | 4630 | 4850 | 0.2978 | 7.81 |

Number of Vibrators | Series Resonance Frequency/f_{s} (Hz) | Parallel Resonance Frequency/f_{p} (Hz) | Electromechanical Coupling Coefficient/k_{e} | Maximum Displacement/S_{m} (10^{−11} m) |
---|---|---|---|---|

1 | 4705 | 4925 | 0.295 | 3.389 |

2 | 4703 | 4923 | 0.295 | 3.388 |

3 | 4705 | 4925 | 0.295 | 3.390 |

4 | 4703 | 4923 | 0.295 | 3.390 |

5 | 4705 | 4925 | 0.295 | 3.389 |

Type | Series Resonance Frequency/f_{s} (Hz) | Parallel Resonance Frequency/f_{p} (Hz) | Electromechanical Coupling Coefficient/k_{e} | Maximum Displacement/S_{m} (10^{−11} m) |
---|---|---|---|---|

2-2 | 4628 | 4848 | 0.298 | 7.79 |

ceramic | 4704 | 4924 | 0.295 | 3.39 |

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**MDPI and ACS Style**

Liu, X.; Wang, L.; Zhong, C.; Zhang, Y.; Hao, S.; Sun, R.
Piezoelectric Composite Vibrator with a Bilaminated Structure for Bending Vibration. *Appl. Sci.* **2019**, *9*, 4191.
https://doi.org/10.3390/app9194191

**AMA Style**

Liu X, Wang L, Zhong C, Zhang Y, Hao S, Sun R.
Piezoelectric Composite Vibrator with a Bilaminated Structure for Bending Vibration. *Applied Sciences*. 2019; 9(19):4191.
https://doi.org/10.3390/app9194191

**Chicago/Turabian Style**

Liu, Xia, Likun Wang, Chao Zhong, Yanjun Zhang, Shaohua Hao, and Ruiqing Sun.
2019. "Piezoelectric Composite Vibrator with a Bilaminated Structure for Bending Vibration" *Applied Sciences* 9, no. 19: 4191.
https://doi.org/10.3390/app9194191