# Ultrasonic Guided Wave Signal Based Nondestructive Testing of a Bonded Composite Structure Using Piezoelectric Transducers

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## Abstract

**:**

## 1. Introduction

- A sandwich plate with Nomex core and single-sided adhesively bonded aluminum facet is studied experimentally, numerically, and analytically.
- SEM study with PZT SONOX P502 parameters is studied with a single-sided adhesively bonded composite structure (ACS).
- The SLDV full wavefield result is compared with the SEM result.
- The elliptical method is applied to the data obtained from SLDV and SEM.
- The elliptical signal method is not limited to the first time of arrival and does not use the differential signals.

## 2. Numerical and Experimental Process

_{33}, d

_{31}, d

_{15}are charge constants; $\frac{{\mathsf{\epsilon}}_{33}^{\mathrm{T}}}{{\mathsf{\epsilon}}_{0}},\frac{{\mathsf{\epsilon}}_{11}^{\mathrm{T}}}{{\mathsf{\epsilon}}_{0}}$ are relative permittivity values; S

_{11}

^{E}, S

_{33}

^{E}are elastic compliance values; ρ represents the density value; ${\eta}_{13}$ represents the Poisson ratio. The manufacturer of the PZT provided all of the properties [20].

## 3. Results and Discussion

#### 3.1. Analysis of the Results from the SLDV

#### 3.2. Analysis of the Results Using Numerically Based Spectral Element Code

#### 3.3. Analysis of the Results Using an Elliptical Based Signal Processing Method

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) ACS plate with damages; (

**b**) zoomed image of BVID 2; (

**c**) cross-section of the plate with the core; (

**d**) Nomex core attached at the backside of the plate and region where a hole and BVIDs were made.

**Figure 2.**(

**a**) Schematic representation of PZT, damage zones; (

**b**) a hole of Ø 0.5 cm detected at 29 μs; (

**c**) BVID 1 detected at 37 μs; (

**d**) BVID 2 detected at 48 μs.

**Figure 3.**(

**a**) Mesh arrangement and PZT position in SEM; (

**b**) hole of Ø 0.5 cm detected at 29 μs for 150 kHz excitation.

**Figure 6.**Experimental case: (

**a**) case 1 quadrant I–IV arrangement of sensors; (

**b**) elliptical method on case 1; (

**c**) elliptical method on case 2; (

**d**) elliptical method on case 3; (

**e**) case 4 quadrant II arrangement of sensors; (

**f**) elliptical method on case 4.

**Figure 7.**Numerical cases: (

**a**) case 5 quadrant I–IV arrangement of sensors; (

**b**) elliptical method on case 5; (

**c**) case 6 quadrant II arrangement of sensors; (

**d**) elliptical method on case 6.

**Table 1.**Experimental table with measurements performed in the scanning laser Doppler vibrometry (SLDV).

No. of Cycles | Frequency (kHz) | Excitation Voltage (Vpp) | Grid Points | Sampling Period (μs) |
---|---|---|---|---|

10 | 150 | 16 × 20 | 411 × 415 | 0.78125 |

Material | Young’s Modulus (GPa) | Poisson Ratio | Density (kg/m^{3}) |
---|---|---|---|

Nomex | 9 | 0.30 | 1384 |

Aluminum | 68 | 0.33 | 2600 |

d_{33} (C/N) | d_{31} (C/N) | d_{15} (C/N) | $\frac{{\mathsf{\epsilon}}_{\mathbf{33}}^{\mathbf{T}}}{{\mathsf{\epsilon}}_{\mathbf{0}}}$ | $\frac{{\mathsf{\epsilon}}_{\mathbf{11}}^{\mathbf{T}}}{{\mathsf{\epsilon}}_{\mathbf{0}}}$ |
---|---|---|---|---|

440 × 10^{−12} | −185 × 10^{−12} | 560 × 10^{−12} | 1850 | 1950 |

S_{11}^{E} (m^{2}/N) | S_{33}^{E} (m^{2}/N) | ${\mathbf{\eta}}_{\mathbf{13}}$ | ρ (_{kg/m}^{3}) |
---|---|---|---|

18.5 × 10^{−12} | 20.7 × 10^{−12} | 0.44 | 7740 |

No. of Cycles | Frequency (kHz) | Grid Points | Sampling Period (μs) |
---|---|---|---|

10 | 150 | 251 × 251 | 6.1 × 10^{−3} |

Frequency (kHz) | Hole (µs) | BVID 1 (µs) | BVID 2 (µs) |
---|---|---|---|

150 | 29 | 37 | 48 |

Case | Test | Sensor Placement | No. of Sensing Points |
---|---|---|---|

1 | Experimental | Quadrant I, II, III, IV | 8 |

2 | Experimental | Quadrant I, II | 4 |

3 | Experimental | Quadrant III, IV | 4 |

4 | Experimental | Quadrant II | 6 |

5 | Numerical | Quadrant I, II, III, IV | 8 |

6 | Numerical | Quadrant II | 6 |

Cases Studied | Group Velocity [m/s] at 0° | Group Velocity [m/s] at 90° |
---|---|---|

Case 4 | 2048 | 2108 |

Case 6 | 2410 | 2365 |

Experimental | Damage Map Maximum Location (cm, cm) | Coordinates of Damage Center (cm, cm) | Error in Estimation (cm) |
---|---|---|---|

Case 1 | (35, 26.5) | (33.0, 25.0) | 2.50 |

Case 2 | (28.9, 41.4) | (29.1, 36.2) | 5.20 |

Case 3 | (27.7, 6.7) | (26.0, 9.0) | 2.80 |

Case 4 | (34.4, 23.0) | (33.0, 25.0) | 2.44 |

Numerical | Damage Map Maximum Location (cm, cm) | Coordinates of Damage Center (cm, cm) | Error in Estimation (cm) |
---|---|---|---|

Case 5 | (29.8, 27.7) | (33.0, 25.0) | 4.10 |

Case 6 | (31.9, 26.0) | (33.0, 25.0) | 1.49 |

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**MDPI and ACS Style**

Balasubramaniam, K.; Sikdar, S.; Fiborek, P.; Malinowski, P.H.
Ultrasonic Guided Wave Signal Based Nondestructive Testing of a Bonded Composite Structure Using Piezoelectric Transducers. *Signals* **2021**, *2*, 13-24.
https://doi.org/10.3390/signals2010002

**AMA Style**

Balasubramaniam K, Sikdar S, Fiborek P, Malinowski PH.
Ultrasonic Guided Wave Signal Based Nondestructive Testing of a Bonded Composite Structure Using Piezoelectric Transducers. *Signals*. 2021; 2(1):13-24.
https://doi.org/10.3390/signals2010002

**Chicago/Turabian Style**

Balasubramaniam, Kaleeswaran, Shirsendu Sikdar, Piotr Fiborek, and Pawel H. Malinowski.
2021. "Ultrasonic Guided Wave Signal Based Nondestructive Testing of a Bonded Composite Structure Using Piezoelectric Transducers" *Signals* 2, no. 1: 13-24.
https://doi.org/10.3390/signals2010002