An enhanced frequency-shift-based damage identification method using tunable piezoelectric transducer circuitry

Frequency-shift-based structural damage identification has been explored extensively in recent years. The performance of current practices, however, is still limited for several reasons, one of which is that the number of measurable modal frequencies is usually much smaller than the number of system parameters required to characterize the damage. In this study, the state of the art of frequency-shift-based damage identification is advanced by incorporating a tunable piezoelectric transducer circuitry into the structure to enrich the modal frequency measurements, meanwhile implementing a high-order identification algorithm to sufficiently utilize the enriched information. By integrating tunable piezoelectric transducer circuitry into the structure, we can introduce additional resonant peaks into the system frequency response function, and these additional peaks can be placed/adjusted over the frequency band by tuning the inductance. Clearly, a significantly increased amount of frequency shift information can be expected to reflect the damage effect. An iterative second-order perturbation-based algorithm in conjunction with an optimization scheme is then used to find the damaged-induced stiffness parameter reduction based on the system eigenvalue changes (frequency shift) before and after the structural damage occurrence. The major advantage of using this algorithm is that it takes into account the damage-induced mode shape changes without the actual measurement of the modes. In a benchmark example, a series of analyses using a cantilever beam integrated with a tunable piezoelectric transducer circuitry is carried out to demonstrate this proposed methodology and verify the performance. It is shown that the modal frequencies can be greatly enriched by inductance tuning, which, together with the high-order identification algorithm, leads to a fundamentally improved performance on the identification of single and multiple damages with the usage of only lower-order frequency measurements.