Exact solution of Euler-Bernoulli equation for acoustic black holes via generalized hypergeometric differential equation. (21st July 2019) - Lee, Jae Yeon; Jeon, Wonju
Abstract: Acoustic black hole (ABH), a thin wedge-shaped structure tapered according to the power-law of power ( m ) greater than or equal to two, has received much attention to the researchers in wave dynamics due to its potential as a light and effective absorber of elastic waves propagating in beams or plates. In this paper, the Euler-Bernoulli equation for the ABH is reformulated into the form of a generalized hypergeometric differential equation for m > 2. Then, the exact solution is derived in terms of generalized hypergeometric functions ( p F q ) where p = 0 and q = 3 by dividing the power m into four cases. The derived exact solution is in linearly independent and regular form for arbitrary m . In addition, by using the exact solution, the displacement field of a uniform beam with an ABH and the reflection coefficient from an ABH are calculated to demonstrate the applicability of the present exact solution. This paper aims at providing a mathematical and theoretical basis for the study of the ABHs.