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Piezoelectric ceramic Lead Zirconate Titanate (PZT) transducers, working on the principle of electromechanical impedance (EMI), are increasingly applied for structural health monitoring (SHM) in aerospace, civil and mechanical engineering. The PZT transducers are usually surface bonded to or embedded in a structure and subjected to actuation so as to interrogate the structure at the desired frequency range. The interrogation results in the electromechanical admittance (inverse of EMI) signatures which can be used to estimate the structural health or integrity according to the changes of the signatures. In the existing EMI method, the monitored structure is only excited by the PZT transducers for the interrogating of EMI signature, while the vibration of the structure caused by the external excitations other than the PZT actuation is not considered. However, many structures work under vibrations in practice. To monitor such structures, issues related to the effects of vibration on the EMI signature need to be addressed because these effects may lead to misinterpretation of the structural health. This paper develops an EMI model for beam structures, which takes into account the effect of beam vibration caused by the external excitations. An experimental study is carried out to verify the theoretical model. A lab size specimen with different external excitations is tested and the effect of vibration on EMI signature is discussed.

The EMI method has emerged as a widely recognized technique for dynamic identification and health monitoring of structural systems. The electromechanical admittance response of the smart system is derived from the dynamic interaction between the PZT transducer and the host structure. The EMI method has been proven direct and easy to implement. The method is typically applied using an electrical impedance analyzer, which scans a predetermined frequency range band in the order of tens to hundreds of kHz. In doing so, the complex admittance or impedance spectrum may be recorded and meaningful information containing the physical properties of the structure may be extracted. For SHM applications, these spectra can be compared at various times during the service lifespan of the structure, with which any change between the spectra is an indication of the presence of damage or material deterioration.

Essentially the EMI method is founded upon the wealth of research accumulated from the modeling studies on electromechanical interaction between the structure and the PZT transducer, which started about two decades ago. Liang

However, the existing EMI method does not consider the structural vibration caused by the external excitation other than the PZT actuation, which means that the existing EMI method is only applicable to the static structures. Unfortunately, many structures are subjected to vibrations in practice. The vibrations of the structures will influence the results of SHM by causing the changes in PZT signatures. The changes in PZT signatures caused by the external excitation and the structural damage must be differentiated such that the correct information of structural health can be obtained. Therefore, this paper studies the effect of vibration on PZT signature by developing a new EMI model for beam structures with external excitations. Furthermore, experimental tests are carried out to verify the developed model.

As mentioned previously, the EMI method has been applied for the structures without excitations. However, no further research has been conducted for the EMI modeling of structures with excitations. This part will focus on the theoretical derivations of EMI models with excitations including both extensional and transverse vibrations. Uniform beams with simply supported boundary conditions will be considered.

The equation of motion for the extensional vibration subjected to distributed force of an Euler-Bernoulli thin beam is given as:
_{s}_{s}_{s}b_{s}_{s}_{s}_{s}_{s}

For a simply supported beam whose strains at two ends are zero, the boundary conditions are:

The equation of motion for the transverse vibration of the same beam is given as:

For a simply supported beam whose displacements and bending moments at two ends are zero, the boundary conditions are:

Based on small displacement assumption, the following displacement field is defined for the extensional displacement of a generic point on the surface of the beam:

Therefore, the total extensional displacement is:

Hence, based on response compatibility, the total induced displacement of the PZT transducer is equal to the displacement difference between two discrete points on the surface of the beam, coincident to the ends of the transducer:
_{1} and _{2} are the coordinates of the two ends of the PZT transducers, as shown in

Consequently, the total displacement of the PZT transducer is:

The following is the displacement of PZT vibration subjected to an electric potential:
_{PZT}_{u}_{w}_{s}_{PZT}

Finally, we can obtain the electromechanical admittance of the PZT transducer:
_{str}K_{PZT}^{−1} is the stiffness ratio; _{str}

In order to verify the developed theoretical model, an experimental test is carried out on an aluminum beam bonded with one PZT transducer. The instruments and equipments used in this experiment are shown in

The HP4192A Analyzer [

The simply supported beam specimen is shown in

As presented in the previous part, the theoretical derivation has been conducted to obtain the final result of the electromechanical admittance for a simply supported beam. And for practical cases, the transverse vibration of the beam is much more critical compared with the extensional vibration. Therefore, only the transverse vibration is considered in the experimental test. Then the electromechanical admittance of PZT can be simplified from

The above equation is applied to obtain the electromechanical admittance over the range of frequency bands. After substituting the values of various parameters into the theoretical formulation and a series of calculations by means of Matlab program, the theoretical results can be obtained. With the change in frequency and magnitude of the excitation force, the electromechanical admittance will change accordingly. Therefore, we will discuss the influence of these two factors.

To verify the developed EMI model, we first compared the predicted peak locations with the experimental ones. The peak locations for two different excitations are listed in

In addition, we introduce damage in the specimen in the experimental test. This attempt is made to compare the peak shifts caused by damage and those caused by external excitation. The conductances for four cases (S1, S2, S3 and S4) are shown in

_{PZT}_{PZT}_{PZT}_{PZT}_{PZT}_{PZT}_{PZT}

It is worth mentioning that we have focused on the peak location and peak shift because in the EMI technique, peak locations represent the natural frequencies of the host structure. Therefore peak shifts in admittance signature indicate the change of structural properties, which may be caused by damage or vibration. Other statistical method such as the root mean square deviation (RMSD) can also be used to analyze the signature [

Although piezoelectric material has been successfully used for structural damage detection in many areas, the influence of the external excitations on the signature of PZT needs further study. This paper aims at ascertaining the effect of external excitation (vibration) on the PZT signature. The fundamental formulation of EMI model is first derived for a simply supported beam with external excitations. In the experiments, an aluminum beam specimen bonded with a PZT sensor is tested. The admittance signatures of the PZT sensor are measured for various excitations. The experimental results are compared with the theoretical predictions to investigate the reliability of the model. Overall, the theoretical model is capable of predicting the resonant peaks in the admittance signature. Further experimental tests are carried out to compare the effects of excitation and damage on the admittance signature. And the effective frequency range of external excitation is studied by the developed model. It is concluded that the effect of external excitation (vibration) on PZT admittance signature could not be neglected if the external excitation frequency and PZT's actuation frequency are comparable. For structural damage assessment, further study on how to eliminate this effect is needed.

A simply supported beam bonded with a PZT transducer.

EMI measurement system.

External excitation system.

Beam specimen with PZT transducer and mini-shaker

Theoretical prediction of PZT admittance for different excitation frequencies.

Theoretical prediction of PZT admittance for different excitation magnitudes.

Errors between theoretical and experimental results.

Theoretical and experimental result of PZT admittance with external force F=1.5sin (1000πt).

Theoretical and experimental result of PZT admittance with external force F=1.6sin (100πt).

Experimental result of PZT admittance for four cases (S1–S4).

Theoretical prediction of PZT admittance for different excitation frequencies (F=0.5sin

Properties of PZT transducer.

^{3}) |
_{31} |
||||||
---|---|---|---|---|---|---|---|

68.9 | 0.001 | 7800 | -2.10E-10 | 2.36E-08 | 1.47E-02 | 100 |

Properties of beam specimen.

^{3} ) |
||||||
---|---|---|---|---|---|---|

200 | 30 | 2 | 68.9 | 0.3 | 2700 | 0.005 |

Theoretical and experimental peak locations for F=1.5sin (1000πt) and F=1.6sin (100πt).

| |||||
---|---|---|---|---|---|

| |||||

Theoretical predictions | Experimental results | Errors | Theoretical predictions | Experimental results | Errors |

| |||||

12.25 | 11.80 | -0.45 | 12.10 | 11.95 | -0.15 |

13.75 | 14.25 | +0.50 | 14.60 | 14.60 | 0 |

18.50 | 17.00 | -1.50 | 15.90 | 16.50 | +0.60 |

21.30 | 20.50 | -0.80 | 21.15 | 20.55 | -0.60 |

24.75 | 25.20 | +0.55 | 25.60 | 25.35 | -0.25 |

27.25 | 27.00 | -0.25 | 26.70 | 26.70 | 0 |

30.55 | 30.15 | -0.40 | 30.25 | 30.30 | +0.05 |

34.55 | 34.75 | +0.20 | 32.40 | 32.35 | -0.05 |

37.40 | 36.00 | -1.40 | 34.85 | 34.75 | -0.10 |

38.50 | 38.30 | -0.20 | 36.90 | 36.65 | -0.25 |

40.00 | 39.85 | -0.15 | 38.25 | 38.25 | 0 |

43.40 | 42.50 | -0.90 | 40.95 | 40.00 | -0.95 |

44.50 | 43.75 | -0.75 | 42.45 | 43.65 | +1.20 |

45.55 | 45.00 | -0.55 | 44.10 | 44.10 | 0 |

46.70 | 46.70 | 0 | 45.00 | 45.00 | 0 |

47.75 | 46.50 | -1.25 |

Peak locations and shifts [unit: kHz].

| |||||||||
---|---|---|---|---|---|---|---|---|---|

S1 | 11.5 | 18 | 22 | 27.5 | 30 | 34 | 35 | 38.5 | 41 |

S2 | 11.5 | 17 | 21.5 | 27 | 30 | 33.5 | 35.5 | 39.5 | 42.5 |

S3 | 12.5 | 17 | 21 | 25.5 | 30.5 | 34.5 | 36.3 | 39.5 | 42 |

S4 | 12.3 | 16.2 | 20.2 | 25 | 30.5 | 34.2 | 36.3 | 40.2 | 43.5 |

S2–S1 | 0 | -1 | -0.5 | -0.5 | 0 | -0.5 | +0.5 | +1 | +1.5 |

S3–S1 | +1 | -1 | -1 | -2 | +0.5 | +0.5 | +1.3 | +1 | +1 |

S4–S2 | +0.8 | -0.8 | -1.3 | -2 | +0.5 | +0.7 | +0.8 | +0.7 | +1 |