On the existence of antisymmetric or symmetric Lamb waves at nonlinear higher harmonics

This article theoretically studies the symmetry characteristics of Rayleigh–Lamb guided waves in nonlinear, isotropic plates. It has been known that the nonlinearity driven double harmonic in Lamb waves does not support antisymmetric motion. However, the proof of this has not been obvious. Moreover, little is known on nonlinearity driven Lamb harmonics higher than double. These gaps were here studied by the method of perturbation coupled with wavemode orthogonality and forced response. This reduced the nonlinear problem to a forced linear problem which was subsequently investigated to formulate an energy level constraint as the defining factor for the absence of antisymmetry at any order of higher harmonic. This constraint was then used to explain the reason behind the absence of antisymmetric Lamb waves at the double harmonic. Further, it was shown that antisymmetric motion is prohibited at all the higher order even harmonics, whereas all the higher order odd harmonics allow both symmetric and antisymmetric motions. Finally, experimental results corroborating theoretical conclusions are presented.