Bandgap Properties of Two-Layered Locally Resonant Phononic Crystals

Multi-layered locally resonant phononic crystals (LRPCs) with wider and multiple bandgaps (BGs) in low frequency range and small size of the unit cell have promising applications in noise and vibration controls. In this paper, a 2D two-layered ternary LRPC consisting of a periodical array of cylindrical inclusions embedded in an epoxy matrix is investigated by the finite element method (FEM), where the inclusion is comprised of two coaxial cylindrical steel cores with rubber coating. It is found that the size of the inclusion of the 2D two-layered ternary LRPC has significant effects on the BG properties. With the increase of the core radius and coating thickness, the first BG would shift to lower frequency range with its width decreasing, and the second BG width would become wider until the third BG appears. Especially, with the increase of the coating thickness, more bands and BGs would appear in the lower frequency range. Based on the formation mechanisms of the BGs, several mass-spring models to predict the frequencies of the first two BG edges are developed. The results calculated by these mass-spring models are in good agreement with those by the FEM except for the upper edge frequency of the second BG when the rubber coating thickness exceeds a certain value and the third BG is opened up. These proposed mass-spring models would allow for quick pre-estimation of the resonance frequencies, and facilitate the selection of possible parameters for the wider and lower frequency BGs to obtain the desired attenuation bands. The studies would also benefit the design of multiple BGs for some device applications.