A Notched Bar as a Vibrational Black Hole

Abstract

A vibrational black hole (VBH) is a slowing structure that decreases wave propagation velocity to zero at a finite distance. In this case, the wave propagation time over this distance becomes infinite. A new structure that approximates the VBH effect for flexural waves is considered. This is a bar/plate with notches the depth of which gradually increases. The flexural stiffness of such a structure gradually decreases with retention of a constant bulk weight. The dependences of parameter variations were found for which the structure acts similarly to a VBH, and the corresponding equation has an exact analytic solution.