Modal displacement method for extracting the bending wave bandgap of plate-type acoustic metamaterials

To directly extract the bending wave bandgap of plate-type acoustic metamaterials, a modal displacement method is proposed. This method could replace the qualitative mode analysis with a quantitative statistical averaged mode displacement of the frame, in order to quantitatively extract the bandgap. Most importantly, the modal displacement method can reveal the mechanism behind a behavior wherein the mode evolution leads to the shifting of the upper edge of the bandgap—identifying this mechanism could correct misjudgment of the upper edge of the bending bandgap in the vibration mode analysis.