Derivation and Validation of Bandgap Equation Using Serpentine Resonator

Bandgap refers to a frequency band where free waves do not propagate. One of the characteristics of a bandgap is its ability to block the propagation of bending waves in a specific frequency band with a periodic structure. Additionally, it has been reported in previous studies that the vibration-reduction performance of a bandgap is superior to that of other reduction methods. A bandgap can be generated in various frequency bands through a simple parameter change in the unit structure. However, the bandgap for a desired frequency band can be determined accurately only with intensive simulations. To overcome this limitation, we have mathematically derived the bandgap using a serpentine spring as a unit structure. The bandgap equation is derived from the general mass–spring system and the final bandgap is derived by substituting the system into the serpentine resonator. The error map for the major design parameter is confirmed by comparing the derived bandgap with the simulation result. In addition, the theoretical bandgap is compared to the experiment value and the vibration-reduction performance of the serpentine resonator is also confirmed. Based on the theoretical and experimental result, the proposed serpentine resonator verifies that the bandgap can be derived mathematically without numerical analysis. Therefore, serpentine resonator is expected to have various applications since it dramatically reduces the time and cost for forming the bandgap of the desired frequency band.