Multiwave non-linear couplings in elastic structures: Part 1. One-dimensional examples

This short contribution has for main purpose to exhibit the essentials of non-linear wave properties in mechanical systems of engineering origin (structural members). Non-linear resonance is examined on two one-dimensional examples, an infinite straight elastic bar and a thin elastic circular ring, exhibiting continuous and discrete spectra, respectively. Three-wave and four-wave interactions and the stability of coupled modes with respect perturbations are discussed, the emphasis being placed on mechanical phenomena (e.g., stress amplification), although analogies with some non-linear optical systems are obvious