Evaluation of systems containing negative stiffness elements for vibration and shock isolation

The research presented in this thesis focuses on the modeling, design, and experimentation of systems containing negative stiffness mechanisms for both vibration and shock isolation. The negative stiffness element studied in this research is an axially compressed beam. If a beam is axially compressed past a critical value, it becomes bistable with a region of negative stiffness in the transverse direction. By constraining a buckled beam in its metastable position through attaching a stiff linear spring in mechanical parallel, the resulting system can reach a low level of dynamic stiffness and therefore provide vibration isolation at low frequencies, while also maintaining a high load-carrying capacity. In previous research, a system containing an axially compressed beam was modeled and tested for vibration isolation [7]. In the current research, variations of this model were studied and tested for both vibration and shock isolation. Furthermore, the mathematical model used to represent the compressed beam in [7] was improved and expanded in current research. Specifically, the behavior exhibited by buckled beams of transitioning into higher-mode shapes when placed under transverse displacement was incorporated into the model of the beam. The piecewise, nonlinear transverse behavior exhibited by a first-mode buckled beam with a higher-mode transition provides the ability of a system to mimic an ideal constant-force shock isolator. Prototypes manufactured through Selective Laser Sintering were dynamically tested using a shaker table. Vibration testing confirmed the ability of a system containing a constrained negative stiffness element to provide enhanced vibration isolation results with increasing axial compression on a beam. However, the results were limited by the high sensitivity of buckled beam behavior to geometrical and boundary condition imperfections. Shock testing confirmed the ability of a system containing a buckled beam with a higher-mode transition to mimic the theoretically ideal constant-force shock isolator.