Modeling of Nonlinear Guided Waves and Applications to Structural Health Monitoring

Abstract

Propagation of nonlinear waves in solid waveguides is a branch of wave mechanics that has received ever-increasing interest in the last few decades. Nonlinear guided waves are promising candidates for interrogating long waveguide-like structures as they conveniently combine high sensitivity to peculiar structural conditions (defects, quasi-static loads, instability conditions), typical of nonlinear parameters, with large inspection ranges, characteristic of wave propagation in confined media. However, the mathematical framework governing the nonlinear guided wave phenomena becomes extremely difficult when characterized to waveguides that are complex in either material (damping, anisotropy, heterogeneous, and the like) or geometry (multilayers, geometric periodicity, and the like). Therefore, the successful use of nonlinear guided waves as a structural diagnostic tool is not always a trivial task. In particular, the efficiency of nonlinear structural health monitoring (SHM) techniques based on higher-harmonics generation (harmonics generated by a monochromatic input in nonlinear waveguides) strongly relies on the correct identification of favorable combinations of primary and resonant double-harmonic nonlinear wave modes for which the nonlinear response is cumulative. The present work develops predictions of nonlinear second-harmonic generation and identifies these combinations of wave modes in complex waveguides by extending the classical semianalytical finite-element formulation to the nonlinear regime, and implementing it into a highly flexible, yet very powerful, commercial finite-element code. The proposed algorithm is benchmarked for four case studies, including a railroad track, a viscoelastic plate, a composite quasi-isotropic laminate, and a reinforced concrete slab. In all these cases, this tool successfully identified appropriate combinations of resonant guided modes (satisfying synchronism and large cross-energy transfer). These results open up new possibilities for the analysis of dispersion and resonance conditions for a variety of complex structural waveguides that do not lend themselves to alternative analyses, such as purely analytical solutions.