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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. 

Soft pneumatic actuators have become indispensable for many robotic applications due to their reliability, safety, and design flexibility. However, the currently available actuator designs can be challenging to fabricate, requiring labor-intensive and time-consuming processes like reinforcing fiber wrapping and elastomer curing. To address this issue, we propose to use simple-to-fabricate kirigami skins—plastic sleeves with carefully arranged slit cuts—to construct pneumatic actuators with pre-programmable motion capabilities. Such kirigami skin, wrapped outside a cylindrical balloon, can transform the volumetric expansion from pneumatic pressure into anisotropic stretching and shearing, creating a combination of axial extension and twisting in the actuator. Moreover, the kirigami skin exhibits out-of-plane buckling near the slit cut, which enables high stretchability. To capture such complex deformations, we formulate and experimentally validates a new kinematics model to uncover the linkage between the kirigami cutting pattern design and the actuator’s motion characteristics. This model uses a virtual fold and rigid-facet assumption to simplify the motion analysis without sacrificing accuracy. Moreover, we tested the pressure-stroke performance and elastoplastic behaviors of the kirigami-skinned actuator to establish an operation protocol for repeatable performance. Analytical and experimental parametric analysis shows that one can effectively pre-program the actuator’s motion performance, with considerable freedom, simply by adjusting the angle and length of the slit cuts. The results of this study can establish the design and analysis framework for a new family of kirigami-skinned pneumatic actuators for many robotic applications. 

Abstract This study investigates the programming of elastic wave propagation bandgaps in periodic and multi‐stable metamaterials by intentionally and uniquely sequencing its constitutive mechanical bits. To this end, stretched kirigami is used as a simple and versatile testing platform. Each mechanical bit in the stretched kirigami can switch between two stable equilibria with different external shapes (aka. “(0)” and “(1)” states). Therefore, by designing the sequence of (0) and (1) bits, one can fundamentally change the underlying periodicity and thus program the phononic bandgap frequencies. This study develops an algorithm to identify the unique periodicities generated by assembling “n‐bit strings” consisting ofnmechanical bits. Based on a simplified geometry of thesen‐bit strings, this study also formulates a theory to uncover the rich mapping between input sequencing and output bandgaps. The theoretical prediction and experiment results confirm that the (0) and (1) bit sequencing is effective for programming the phonic bandgap frequencies. Moreover, one can additionally fine‐tune the bandgaps by adjusting the global stretch. Overall, the results of this study elucidate new strategies for programming the dynamic responses of architected material systems.