The paper presents application of a modified, symmetrical Bouc-Wen model to simulate the mechanical behaviour of high-frequency piezoelectric actuators (PAs). In order to identify parameters of the model, a two-step algorithm was developed. In its first stage, the mechanical parameters were identified by taking into account their bilinear variability and using a square input voltage waveform. In the second step, the hysteresis parameters were determined based on a periodic excitation. Additionally, in order to reduce the influence of measurement errors in determination of selected derivatives the continuum wavelet transform (CWT) and translation-rotation transformation (TRT) methods were applied. The results proved that the modified symmetrical Bouc-Wen model is able to describe the mechanical behaviour of PAs across a wide frequency range.

Early detection of damage is necessary for the safe and reliable use of civil engineering structures made of concrete. Recently, the identification of micro-cracks in concrete has become an area of growing interest, especially when it comes to using wave-based techniques. In this paper, a non-destructive testing approach for the characterization of the fracture process was presented. Experimental tests were performed on concrete beams subjected to mechanical degradation in a 3-point bending test. Ultrasonic waves were registered on a specimen surface by piezoelectric transducers located at several points. Then, the signals were processed taking advantage of wave scattering due to micro-crack disturbances. For early-stage damage detection, coda wave interferometry was used. The novelty of the work concerns the application of the complex decorrelation matrix and the moving reference trace approach for better distinguishment of sensors located in different parts of a crack zone. To enhance coda wave-based damage identification results, optical imaging of crack development was performed by means of digital image correlation measurement. The results obtained showed that the coda wave interferometry technique can be successfully used as a quantitative measure of changes in the structure of concrete. The results also indicated that the course of decorrelation coefficient curves enabled the identification of three stages during degradation, and it depended on the location of acquisition points versus the crack zone.