Elastic-wave transmission through self-similar anisotropic Cantor-like multilayers
1 University of Bordeaux, I2M-APY, UMR 5295 - 33405 Talence, France
2 University of Toulouse, Laboratoire PHASE - 31062 Toulouse, France
Received: 26 February 2016
Accepted: 25 April 2016
Through the study of elastic wave propagation in Cantor-like anisotropic multilayers, this work analyzes the influence of medium geometry on the transmission of elastic waves to yield a better understanding of the connection between topological ordering and physical properties. Cantor-like multilayers, whose homothetic dimension is modified by changing the length of the central segment, are made of one anisotropic material with two orientations. The influence of the combination of self-similarity and anisotropy on the global transmission is investigated by means of iteration order, homothetic dimension and layer orientations. The propagation is described by the stiffness matrix algorithm. The results reveal that the homothetic dimension scales the resonance frequencies and the frequency ranges of the pseudo band gaps, and that layer orientation influences the speed of quasi-transverse waves to enhance the effect of self-similarity. Finally, an extensive study on various frequency ranges is conducted. It is demonstrated that self-similarity may be used to tune the position and the width of the pseudo band gaps to minimize the global acoustic transmission.
PACS: 43.20.Gp – Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves / 43.35.Gk – Phonons in crystal lattices, quantum acoustics / 62.30.+d – Mechanical and elastic waves; vibrations
© EPLA, 2016