Higher harmonic generation in nonlinear waveguides of arbitrary cross-section

Abstract

This article concerns the generation and properties of double harmonics in nonlinear isotropic waveguides of complex cross-section. Analytical solutions of nonlinear Rayleigh-Lamb waves and rod waves have been known for some time. These solutions explain the phenomenon of cumulative double harmonic generation of guided waves. These solutions, however, are only applicable to simple geometries. This paper combines the general approach of the analytical solutions with semi-analytical finite element models to generalize the method to more complex geometries, specifically waveguides with arbitrary cross-sections. Supporting comparisons with analytical solutions are presented for simple cases. This is followed by the study of the case of a rail track. One reason for studying nonlinear guided waves in rails is the potential measurement of thermal stresses in welded rail.