This study examines the transverse elastic wave propagation bandgap in a buckled kirigami sheet. Kirigami — the ancient art of paper cutting — has become a design and fabrication framework for constructing metamaterials, robotics, and mechanical devices of vastly different sizes. For the first time, this study focuses on the wave propagation in a buckled kirigami sheet with uniformly distributed parallel cuts. When we apply an in-plane stretching force that exceeds a critical threshold, this kirigami sheet buckles and generates an out-of-plane, periodic deformation pattern that can change the propagation direction of passing waves. That is, waves entering the buckled Kirigami unit cells through its longitudinal direction can turn to the out-of-plane direction. As a result, the stretched kirigami sheet shows wave propagation band gaps in specific frequency ranges. This study formulates an analytical model to analyze the correlation between such propagation bandgap and the kirigami geometry. This model first simplifies the complex shape of buckled kirigami by introducing “virtual” folds and flat facets in between them. Then it incorporates the plane wave expansion method (PWE) to calculate the dispersion relationship, which shows that the periodic nature of the buckled kirigami sheet is sufficient to create Bragg scattering propagation bandgap. This study’s results could open up new dynamic functionalities of kirigami as a versatile and multi-functional structural system.

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