On the analysis of contact acoustic nonlinearities caused by sub-surface cracks in vibrating beams
Sprache des Vortragstitels:
91rd Annual Meeting of the International Association of Applied Mathematics and Mechanics
Sprache des Tagungstitel:
This contribution investigates the linear and nonlinear response of a harmonically excited beam which has a local crack in axial direction. The investigation of this idealized problem is motivated by techniques in structural health monitoring (SHM) where the frequency response of a piezoelectric transducer, which is attached on a mechanical structure of interest, is evaluated. The piezoelectric element is excited by a harmonic voltage signal, which causes vibrations of both, the element and the structure. The measured electrical impedance of the piezoelectric element reflects thereby the structural response. Consequently, changes of the impedance indicate structural damages, such as delaminations or debondings in composite materials.
Advanced approaches of the electro-mechanical impedance method aim for nonlinear features in the measured signals. These nonlinearities are supposed to be caused by the clapping of the crack-faces during vibration. The current contribution investigates this phenomenon on hand of the simple problem of a cracked beam. Analytical considerations of reduced models and enhanced numerical finite element simulations show that the unilateral support during opening and closing of the crack may cause measureable higher harmonic responses. Moreover, experiments are presented, where vibrating aluminum beams with artificially introduced cracks are observed with high-frequency laser scanning vibrometry. The vibration at the crack show an amplification signature in the higher harmonic range that can only be assigned to contact acoustic nonlinearities.