Higher order interaction of elastic waves in weakly nonlinear hollow circular cylinders. II. Physical interpretation and numerical results

A plate ray perspective for elastic wave propagation in hollow circular cylinders is presented in order to excite a predominant flexural mode, which in turn generates higher order harmonics due to nonlinear material behavior. The scattering angles are determined for the internally resonant higher order harmonics due to the interactions of two collimated waves. Primary waves that can generate strongly cumulative higher order harmonics are identified for mode self interactions and mutual interactions. A helical inter-digital transducer has been designed for the excitation of a single dominant flexural mode. Numerical evaluations that demonstrate cumulative second harmonic generation are undertaken for both torsional and longitudinal flexural waves. Quadratic sum and difference harmonic generation is observed for the mutual interaction between two primary torsional flexural wave modes.