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

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