Kirigami oscillators: nonlinear free and forced responses

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.