Scattering of flexural waves from a hole in a thin plate with an internal beam

Abstract

The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.

Single-phase metamaterial plates for broadband vibration suppression at low frequencies

“…Following the procedures introduced in Refs. [46,48], we obtain the remaining impedance matrix (see Appendix A)…”

Scattering of flexural waves from an N-beam resonator in a thin plate

“…A detailed account of the basic formulation describing the connection between beam and plate can be found in Ref. 26. Obviously, the displacement, the slope, the moment and shear stress, all of them should be continuous at both anchor points for the n-th beam.…”

“…For the cases considered here, an incident plane wave and a punctual source, the expressions for A ( * ) q can be found elsewhere. [26] Now, the coefficients C…”

“…Particularly, the model here developed is an extension of the impedance matrix method previously used in solving the scattering of flexural waves from a hole with an internal beam. [26] In this paper, a similar procedure is followed to get the transfer matrix (T-matrix) of the complex resonator under study, which lays a foundation on analysing metamaterials with multiple scattering theory.…”

“…where S and T represent complex expressions involving combinations of Bessel functions. Their explicit expressions are available in Ref 26…”