Eur. Phys. J. B 15, 435-443 (2000)
https://doi.org/10.1007/s100510051144

The scattering and transmission of elastic waves in quasi-two-dimensional planar waveguides with linear defect boundaries

¹ Département de Physique, Institut des Sciences Exactes, Université Mouloud Mammeri de Tizi-Ouzou, 15000 Tizi-Ouzou, Algeria
² Laboratoire de Physique de l'État CondenséUPRES-A 6087, Université du Maine, 72085 Le Mans, France
³ Laboratoire d'AcoustiqueUMR 6613, Université du Maine, 72085 Le Mans, France
⁴ Institut de Physique Appliquée, École Polytechnique Fédérale, 1015 Lausanne, Switzerland

Received: 8 November 1999
Revised: 14 January 2000
Published online: 15 June 2000

Abstract

The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants.