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This paper investigates the evolution of EM admittance of piezoelectric transducers mounted on a notched beam from wave propagation perspective. A finite element analysis is adopted to obtain numerical solutions for Lamb waves reverberating on the notched beam. The mode-converted Lamb wave signals due to a notch are extracted by using the polarization characteristics of piezoelectric transducers collocated on the beam. Then, a series of temporal spectrums are computed to demonstrate the evolution of EM admittance through fast Fourier transform of the mode-converted Lamb wave signals which are consecutively truncated in the time domain. When truncation time is relatively small, the corresponding temporal spectrum is governed by the characteristics of the input driving frequency. As truncation time becomes large, however, the modal characteristics of the notched beam play a crucial role in the temporal spectrum within the input driving frequency band. This implies that mode-converted Lamb waves reverberating on the beam contributes to the resonance of the beam. The root mean square values are computed for the temporal spectrums in the vicinity of each resonance frequency. The root mean square values increase monotonically with respect to truncation time for any resonance frequencies. Finally the implications of the numerical observation are discussed in the context of damage detection of a beam.

The Evolution of Electromechanical Admittance from Mode-converted Lamb Waves Reverberating on a Notched Beam