Nonlinear Semianalytical Finite-Element Algorithm for the Analysis of Internal Resonance Conditions in Complex Waveguides

Abstract

Research efforts on nonlinear guided wave propagation have increased dramatically in the last few decades because of the high sensitivity of nonlinear waves to structural conditions (defects, quasi-static loads, instability conditions, and so on). However, the mathematical framework governing the nonlinear guided wave phenomena becomes extremely challenging in waveguides that are complex in either materials (damping, anisotropy, heterogeneous, etc.) or geometry (multilayers, geometric periodicity, etc.). The present work develops predictions of nonlinear second-harmonic generation in complex waveguides by implementing a semianalytical finite-element formulation that accounts for material nonlinearities into a highly flexible, yet very powerful, commercial finite-element code. Once formulated correctly, the proposed analysis can easily take into account damping effects, anisotropic multilayered properties, periodic geometries, and other complex waveguide properties in a computational efficient and accurate manner. Results are presented for the following cases: a railroad track, a viscoelastic plate, a composite quasi-isotropic laminate, and a RC slab. In these cases, favorable 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.