Peridynamic Simulation of Damage Evolution for Structural Health Monitoring
Modal-based methods for structural health monitoring require the identification of characteristic frequencies associated with a structure’s primary modes of failure. A major difficulty is the extraction of damage-related frequency shifts from the large set of often benign frequency shifts observed experimentally. In this study, we apply peridynamics in combination with modal analysis for the prediction of characteristic frequency shifts throughout the damage evolution process. Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture progressive material damage. The application of modal analysis to peridynamic models enables the tracking of structural modes and characteristic frequencies over the course of a simulation. Shifts in characteristic frequencies resulting from evolving structural damage can then be isolated and utilized in the analysis of frequency responses observed experimentally. We present a methodology for quasi-static peridynamic analyses, including the solution of the eigenvalue problem for identification of structural modes. Repeated solution of the eigenvalue problem over the course of a transient simulation yields a data set from which critical shifts in modal frequencies can be isolated. The application of peridynamics to modal analysis is demonstrated on the benchmark problem of a simply-supported beam. The computed natural frequencies of an undamaged beam are found to agree well with the classical local solution. Analyses in the presence of cracks of various lengths are shown to reveal frequency shifts associated with structural damage.