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...

Nonlinear resonant interactions between planar waves in a thin circular ring are investigated. It is found that a high-frequency azimuthal wave is unstable against a pair of secondary low-frequency waves. The secondary waves are of two types; either two bending or azimuthal and bending. These are...

The non-linear resonance coupling in a thin plate in the Kirchhoff-Love approximation is selected as a two-dimensional example of mechanical systems exhibiting a rich range of resonant wave-like phenomena. This is originally examined by use of Whitham's average-Lagrangian method. In...

The first part of the work has concluded that bending waves in a ring, being the low-frequency modes of resonant triplets, are stable against small perturbations. Consequently, on the one hand, a bending wave should behave as a linear quasi-harmonic wavetrain. The first-order approximation...

Nonlinear waves in elastic bar

This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra,...