Ultrawide coupled bandgap in hybrid periodic system with multiple resonators

Mechanical metamaterials can be used to control elastic waves, but it is challenging to obtain multiple or ultrawide bandgaps. A one-dimensional simple periodic system with multi-resonator unit cells can achieve multiple locally resonant bandgaps. A unit cell that comprises multiple cells is called a hybrid unit cell. Two different metamaterials with hybrid unit cells are proposed to achieve a wider coupled bandgap. The first type of metamaterial with a hybrid unit cell comprises two simple cells that have different bandgaps connected by a spring. A new Bragg bandgap appears near the locally resonant bandgaps. By adjusting the spring stiffness, these two types of bandgaps can be coupled to achieve an ultrawide coupled bandgap in a lower frequency range. The second type of metamaterial with a hybrid unit cell comprises two different sub-periodic systems. The bandgaps can be combined to achieve a wider bandgap. With this hybrid periodic system, a wider bandgap can be achieved by designing sub-periodic systems with different bandgaps. In addition, the transmission of a finite periodic system is calculated by the transfer-coefficient method, and the results show that elastic waves can be suppressed in wider frequency range in hybrid periodic systems. This paper provides new ways to design metamaterials with wider and lower bandgaps, which can be used for wide and low-frequency vibration isolation in engineering applications.