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Abstract Inspired by the ancient Japanese art of kirigami, slitted plastic sheets, termed kirigami springs, were designed, fabricated, and characterized, utilizing the quasi-mechanism behavior of various slit patterns. Quasi-static tension tests determined the spring stiffness, and experimental transient responses were analyzed to infer system damping. A system of two parallel-connected kirigami springs, attached to a mass oscillating on a smooth track, was modeled as a 1 DOF Helmholtz-Duffing oscillator with nonlinear damping. The system's free and forced responses were compared to experimental and numerical results using asymptotically valid solutions derived via the Method of Multiple Time Scales. This approach provides an unprecedented degree of programmability in the constitutive relations for nonlinear oscillators and is straightforward to implement. 

In this article we propose a theoretical investigation of the nonlinear dynamical response of a class of planar resonators dubbed the V-Shaped resonator. The resonators are intended for energy harvesting purpose and are designed to exhibit two-to-one internal resonance. In particular, we navigate the design space for the generalized V-shaped resonator to investigate the influence of shape parameters on the performance of the Vibration Energy Harvester. Notably, we introduce two metrics that help elucidating the role of the shape parameter in dictating the behavior of the system in terms of peak voltage and operational bandwidth width. For simplicity, we consider that the system is subjected to harmonic excitations near its primary resonances. 

Abstract Kirigami is defined as the ancient Japanese art of cutting and folding paper to create three-dimensional structures, which is a subset of the larger term. Recent developments in kirigami-based structures have sparked interest in the engineering community for the development of mechanical metastructures with customized behavior such as negative Poisson’s ratio, out-of-plane buckling, and soft robot locomotion. In this manuscript, nonlinear springs based on kirigami are developed; the springs can be used to create customized nonlinear oscillators and vibration suppression systems. A Helmholtz-Duffing oscillator with nonlinear damping is created by attaching a mass to a smooth track with the kirigami springs attached to it. Kirigami springs were made by strategically cutting plastic sheets in predetermined patterns and arranging them in a ring. Identification of the unknown system parameters is accomplished through the use of a two-step procedure. To determine the quasi-static behavior of the spring, it was first subjected to tensile testing. These parameters serve as the foundation for developing a strategy for determining the unknown energy loss parameters in a system. In the second step, the Method of Multiple Scales is used to develop an approximate solution for the transient response, which is then tested. This solution is coupled with an optimization routine that, by modifying the unknown model parameters, seeks to reduce the error between the experimental free oscillations and the developed analytical solution as closely as possible.