The effects of composite primitive cells on band gap property of locally resonant phononic crystal

Locally resonant phononic crystal (LRPC) has the extraordinary property to prohibit the wave propagation in specific low-frequency ranges, however it exists limitation in engineering application due to narrow band gap width. Extensive achievements have been obtained on the locally resonant band gap (LRBG) tunability, whereas existing investigations mainly concern the independent primitive cells structure, which have the limitation in obtaining low-frequency and broadband simultaneously. In this paper, the composited locally resonant phononic crystals (CLRPC) are proposed and the effects of primitive cells contact state on the LRBG properties are investigated. The dispersion curves are applied to obtain the LRBG, and the corresponding modal features are analyzed to explain the band gap formation mechanism. The band structure indicates the design of composite primitive cells is able to increase the band gap number and obtain lower band gap, which is verified by the frequency response function (FRF). For the band gap formation mechanism, the asymmetric vibration due to primitive cells contact leads to diverse and strong coupling response, which generates more band gaps and reduces the band gap starting frequency, therefore the band gaps can be tuned by designing carefully the geometry structure of CLRPC. Further researches on band gap optimization demonstrate that the smaller cell spacing, smaller lattice constant and larger damping of coating layer should be satisfied to obtain broader LRBG and considerable attenuation synchronously. This investigation can provide references for the locally resonant isolation structure design in the low-frequency vibration control field.