On the Design of a Tunable Nonlinear Resonator for Vibration Attenuation

This article presents the design of a tunable nonlinear resonator with shape memory alloys (SMA). An equation for nonlinear mass, damping, and stiffness is derived based on a lumped model consisting of linear springs and rigid bars. It is shown that the resonator can operate as either a stable or bistable system by modifying the stiffness parameters in the model. The selected system exhibits different characteristics, particularly nonlinear damping, which can be increased by adjusting the resonator's frame support parameters. The resonator can achieve different natural frequencies by varying one of the stiffnesses or by applying different magnitudes of base excitation due to its nonlinearity. The physical model is constructed using an SMA beam, preloaded by the flexures of the support frame. By heating the SMA beam, its Young's modulus changes, similar to varying the stiffness of the lumped model, demonstrating that the system can transition between stable and bistable states, with its transmissibility peak varying by approximately 36%. In addition, amplitude-dependent transmissibility peaks are observed for all the temperatures investigated. These findings highlight the potential of SNLRs with embedded SMAs for practical applications in tunable metamaterials, offering adaptable and efficient vibration attenuation.