Unconventional wave reflection due to “resonant surface”

• Published in: Wave motion 2013-06, Vol.50 (4), p.852-868
• Main Authors: Schwan, L., Boutin, C.
• Format: Article
• Language: English
• Subjects: Anisotropy; Boundary layer; Conversion; Depolarization; Engineering Sciences; Half spaces; Homogenization; Homogenizing; Impedance; Mechanics; Oscillators; Resonant surface; Surface impedance; Three dimensional; Wave reflection
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2013.02.010

This study deals with the reflection phenomena in an elastic half-space on which lies a “resonant surface”. The resonant surface consists in a 2D periodic repetition of a surface element over which linear oscillators are distributed. Following the homogenization approach developed by Boutin and Roussillon (2006) [1], the periodic distribution of oscillators (1 to 3D sprung-mass) is reduced to a frequency-dependent surface impedance. It is hereby shown that the surface motion comes to zero in the resonating direction around the oscillators’ eigenfrequency. Further, the surface impedance may be isotropic or anisotropic, according to the type of oscillator. Thereby unusual free/rigid mixed boundary condition arises, which in turn induces atypical reflected wave fields. The most notable effects are (i) drastic change of P and SV waves conversion, (ii) depolarization of shear waves, (iii) conversion of SH waves into P and SV waves, and (iv) possibility of vanishment of the whole reflected field. The physical insight of the theoretical results is discussed and numerical illustrations are provided. •A drastic change of P and SV waves conversion.•The full depolarization of normally-incident shear waves.•The conversion of SH waves into P and SV waves.•The possibility of the whole reflected field to vanish.