Numerical and experimental characterization of pre-fractal anisotropic stacks

Marie-Fraise Ponge , Xavier Jacob , Vincent Gibiat

In this work, propagation in multi-layered anisotropic media is numerically and experimentally investigated. Acoustic properties of pre-fractal samples constituted by a succession of orthotropic layers are studied. Complex media (periodic, disordered or fractal) are known for their remarkable properties as regards to acoustic wave propagation. Fractals appear to be between periodicity and disorder and their intrinsic proportional transformation impacts directly on waves propagation. Indeed, they represent very well natural irregularities, but they are also built from a repetitive pattern at different scales: they are self-similar. The layers orientations in the stack follow a self-similar sequence. It can be demonstrated that such pre-fractal media are similar to periodic structures with defects. The fractal type affects the introduced disorder. Bulk waves propagation in multi-layered anisotropic media is theoretically described by the stiffness matrix method (published by Rokhlin and Wang in 2002). From the resolution of Christoffel equation, stresses and displacements in each layer are connected by a matrix formalism. Pre-fractal stacks are numerically and experimentally characterized. They are also compared with classical fractal, periodic and disordered structures.

Mots clés: Self-similarity; Multi-layered; Anisotropy

Domaines: Acoustique [physics.class-ph]

Marie-Fraise Ponge, Xavier Jacob, Vincent Gibiat. Numerical and experimental characterization of pre-fractal anisotropic stacks. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810924⟩