Branched flows of flexural elastic waves in non-uniform cylindrical shells

TL;DR

This paper demonstrates the existence of branched flows of flexural elastic waves in cylindrical shells with non-uniform properties, revealing universal scaling laws and theoretical insights into wave localization due to structural imperfections.

Contribution

It introduces the first analysis of branched flows in flexural elastic waves in cylindrical shells, deriving and confirming scaling laws through theory, simulations, and finite element analysis.

Findings

High amplitude regions scale with variance and correlation length of stiffness variations.

Scaling laws are derived from ray equations and confirmed by numerical simulations.

Universal exponents observed across different wave types and elastic structures.

Abstract

Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour-consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for other types of waves, as well as flexural and hence dispersive waves in elastic plates.