Higher-Harmonic Generation Analysis in Complex Waveguides via a Nonlinear Semianalytical Finite Element Algorithm

Propagation of nonlinear guided waves is a very attracting phenomenon for structural health monitoring applications that has received a lot of attention in the last decades. They exhibit very large sensitivity to structural conditions when compared to traditional approaches based on linear wave features. On the other hand, the applicability of this technology is still limited because of the lack of a solid understanding of the complex phenomena involved when dealing with real structures. In fact the mathematical framework governing the nonlinear guided wave propagation becomes extremely challenging in the case of waveguides that are complex in either materials (damping, anisotropy, heterogeneous, etc.) or geometry (multilayers, geometric periodicity, etc.). The present work focuses on the analysis of nonlinear second-harmonic generation in complex waveguides by extending the classical Semianalytical Finite Element formulation to the nonlinear regime, and implementing it into a powerful commercial Finite Element package. Results are presented for the following cases: a railroad track and a viscoelastic plate. For these case-studies optimum combinations of primary wave modes and resonant double-harmonic nonlinear wave modes are identified. Knowledge of such combinations is critical to the implementation of structural monitoring systems for these structures based on higher-harmonic wave generation.