Nonlinear guided wave propagation is a field that has received considerable attention in the last few decades mainly because the use of nonlinear features of elastic waves appears very promising for Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) of several structures. Recent findings show that the characteristics of nonlinear wave propagation significantly enhance both sensitivity and efficiency compared to more traditional NDE/SHM approaches. Nonlinear features (in particular higher harmonics generation) may be very efficient indicators of some structural states that are difficult or even impossible to be detected by other means. The complex mathematical framework governing these phenomena is the main obstacle to the widespread diffusion of these techniques; in the past investigations pertaining to higher harmonic generation have been limited in applicability to structures with simple geometries where an analytical solution for the waveguide modes was available. In the present paper the classical Semi-Analytical Finite Element (SAFE) formulation (necessary to analyze complex geometries) is extended to the nonlinear regime and is implemented into a commercial code, exploiting all its capabilities. The resulting tool is able to efficiently study the nonlinear elastic wave propagation and the internal resonance conditions in a broad spectrum of structural systems. After a brief description of the theoretical background and the proposed algorithm, a railroad track is considered as case-study. The nonlinear analysis reveals optimal combinations of primary and secondary modes and also pinpoint “false positives” where internal resonance does not occur. It is emphasized how the knowledge of these ideal combinations of modes is pivotal for the application of any NDE/SHM technique relying on nonlinear features of elastic wave propagation; in light of this fact the formulation proposed in the present work appears very promising.

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