Application of scaled boundary finite element method for vibration-based structural health monitoring of breathing cracks

The dynamic response of the host structure to a high-frequency actuation is usually used for the detection of tiny damage in structures in the form of breathing crack. The simulation of the microcrack’s effect on the response is essential for several damage identification targets. The conventional finite element method suffers from very small mesh size requirements to address the high-frequency problems, resulting in very large mass and stiffness matrices. In this study, the scaled boundary finite element method was applied to model different schemes of structural health monitoring of a structure with breathing cracks based on high-frequency vibration. The scaled boundary finite element method discretizes only the boundary of the model and thus substantially reduces the size of structural matrices. The node-to-node contact strategy was introduced to the scaled boundary finite element method to capture the contact problem that occurs during the vibration of the breathing crack. As breathing crack vibration results in some nonlinear effects, the simulation of three phenomena was of interest: higher harmonic generation, frequency shift, and vibro-acoustic modulation. A shooting method was used for efficient time integration and description of the frequency response function in the nonlinear regime. According to the results, the scaled boundary finite element method is of great power, efficiency, and accuracy to treat the contact problems, especially in high-frequency regimes. Moreover, the nonlinear methods provide certain advantages over the linear techniques in the early detection of incipient damage.