Characterization of Nonlinear Kirigami Springs Through Transient Response

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.