On the existence of longitudinal or flexural waves in rods at nonlinear higher harmonics

This article theoretically studies the conditions for existence of longitudinal or flexural waves in nonlinear, isotropic rods and presents numerical simulations corroborating the theoretical results. It has been known that the existence of guided waves at nonlinearity induced double harmonics is subject to constraints which arise from the potential of power flux transfer from the primary generating mode to the generated higher order modes. The knowledge about the behavior of waves in rods at harmonics higher than double is still limited. This gap was addressed here by the method of perturbation coupled with wavemode orthogonality and forced response. This reduces the nonlinear problem to a forced linear problem which was subsequently investigated to formulate an angular order-based constraint as the condition of existence/nonexistence of nonlinearity-driven higher harmonics of longitudinal and flexural waves in rods.