2022/11/01 by Kevin Jose, Neil M. Ferguson, Jose, Kevin +3
Engineering · #Adhesion, Friction, and Surface Interactions #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fluid Dynamics and Vibration Analysis #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2211.02181
openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.