The locally resonant phononic crystals have low frequency elastic bandgap characteristics and have important application prospects in the field of vibration and noise control. The structure of three-dimensional locally resonant phononic crystals is mainly based on a multi-component material system, which limits its manufacturing and application for practical engineering. Therefore, a three-dimensional phononic crystal structure composed of single-phase material is proposed. The band structure, vibration mode and transmission spectrum of the phononic crystals are calculated by finite element method. The numerical results show that the structure can open a 20% complete bandgap within the range of normalized frequency below 0.1. The local resonance of the spherical mass element and the connectors is the main cause of the bandgap. The change of structural material properties affects the frequency of the bandgap, and the structural geometric parameters determine the relative position of the band gap in the whole band structure. The width and position of phononic band gaps can be manipulated via the materials and geometric parameters of the structure. In addition, the further widening of the band gap can be realized by constructing gradient structures with gradually changing geometric parameters. The three-dimensional structure composed of single-phase material can be used for the design and development of low-frequency vibration and noise reduction materials and devices.
