Concentration of Eigenfrequencies of Elastic Bodies with Blunted Cuspidal Sharpening

The phenomenon of black holes for elastic waves has been investigated for Kirchhoff plates and spatial isotropic deformed bodies with a cuspidal sharpening. Since cusps in real engineering structures are always blunted and, therefore, there is no continuous spectrum triggering wave processes, the main focus of the paper implies studying the behavior of eigenfrequencies of a sharpening with a tiny blunted tip, a decrease in the size of which (h > 0) is interpreted as an improvement in the peak-fabrication quality. Several groups of eigenfrequencies with different behavior at \(h \to + 0\) (namely, hardly movable, gliding, and wandering) are described. The found concentration of eigenfrequencies in a wide spectral range indicates the following novel mechanism of kinetic-energy absorption by a blunted sharpening: trapping of elastic waves at “almost all” frequencies.