Bandgap characteristic and bandgap expansion of a petal-shaped metamaterial

The control of low frequency vibration and noise is an urgent problem. The bandgap characteristic of metamaterials is the key to solve this problem. In this paper, a plum metamaterial structure is designed based on the local resonance theory and its bandgap characteristics are studied and extended. The structure is calculated by finite element method, and its vibration modal characteristics are analyzed. The corresponding spring oscillator equivalent model is established and verified. Plum metamaterial structure has a wide band gap in the low frequency range below 250 Hz. The band gap width is about 177 Hz, and its frequency response function calculation results show that it has good attenuation effect. By changing the material and size parameters of the structure, the low frequency band gap can be adjusted to meet the requirements of practical applications. The influence priority of each parameter is determined by grey correlation analysis method. A phonon -like crystal model is proposed, and the structural design and research results provide a theoretical basis and an effective method for obtaining the low frequency band gap in the study of metamaterials, and have a potential application prospect in the low frequency vibration noise reduction.