Propagation of compressional elastic waves through a 1-D medium with contact nonlinearities

TL;DR

This paper investigates how monochromatic elastic waves propagate through a one-dimensional medium with contact nonlinearities, using theoretical, numerical, and analytical methods to understand harmonic generation and wave behavior across cracks.

Contribution

It introduces a combined theoretical and numerical approach to model wave propagation through nonlinear cracks in 1D media, including perturbation and harmonic balance analyses.

Findings

Cracks induce harmonic generation in wave propagation.

Perturbation analysis estimates mean crack dilatation.

Numerical simulations agree with Bloch-Floquet analysis.

Abstract

Propagation of monochromatic elastic waves across cracks is investigated in 1D, both theoretically and numerically. Cracks are modeled by nonlinear jump conditions. The mean dilatation of a single crack and the generation of harmonics are estimated by a perturbation analysis, and computed by the harmonic balance method. With a periodic and finite network of cracks, direct numerical simulations are performed and compared with Bloch-Floquet's analysis.