Electrical admittance of a circular piezoelectric transducer and chargeless deformation effect

The electromechanical impedance (EMI) method is a promising technique for the sake of structural health monitoring. This method measures the electrical admittance of a piezoelectric transducer attached to a host structure. If the mechanical admittance of the host structure is retrieved from the measured electrical admittance, more information about the host structure can be obtained. For this purpose, an accurate analytical closed-form expression relating the electrical admittance of a piezoelectric transducer to the mechanical admittance of a host structure is needed. Although such expression is available in literature for a circular piezoelectric transducer (CPT), the authors found it erroneous. In this work, closed-form expressions of the mechanical impedance of a free CPT and the electrical admittance of a CPT attached to a host structure are re-defined. Following, the latter is validated by comparing its result with that of an experiment. Successful use of such expressions demands accurate values of the material properties of the transducer. Hereto an analytical-experimental procedure for material calibration of a CPT is proposed. Next, the procedure of detecting the natural frequencies of a host structure using the EMI method is discussed. Using 3D numerical simulations, it is demonstrated that some of the natural frequencies cannot be detected. In essence, the corresponding mode shapes of those natural frequencies impose a deformation onto a CPT which generates a non-significant electric charge