Wave Propagation and Manipulation in Sierpinski Fractal Phononic Crystals

The possibilities of influencing the behavior of propagating waves using the appropriate choice of materials is a field of interest in engineering. Traditional materials have very limited control of sound waves. Thus, new artificial composite materials with good vibration absorbing properties are needed to solve this problem. This paper investigates the band structure and waves modes of a two-dimensional (2-D) Sierpinski fractal phononic crystals (PnC). These PnC consist of various lattice inclusions of one and two materials with large impedance mismatch in a rubber matrix. The inclusions present square and circular cross sections and are concentrically aligned. The chosen materials allow elastic waves to be forbidden from propagation within certain frequency bands, the so-called band gaps or stop bands. Structures with fractal distributions and higher stages favor the appearance of several absolute gaps and with larger bandwidth. The band structure and wave mode shapes are calculated by the Finite Element (FE) and Plane Wave Expansion (PWE) methods, considering the Bloch-Floquet periodic conditions.