Planar analysis of a quasi-zero stiffness mechanism using inclined linear springs

Negative stiffness mechanisms have seen renewed attention in recent years for their ability to reduce the resonance frequency of a structure without impeding their load-bearing ability. Such devices are often described as having quasi-zero stiffness when the negative stiffness is tuned to reduce the overall stiffness of the system as close to zero as possible without creating an instability. The system analysed in this work consists of a vertical spring for load bearing, and two symmetric inclined springs which behave with a snap-through effect to achieve negative stiffness. While this structure has been analysed extensively in the literature, generally only the stiffness in the vertical direction has been considered in the past. Here, the horizontal stiffness is assessed as well, and it is shown that it is possible to achieve quasi-zero stiffness in both directions simultaneously if the spring stiffnesses and pre-loads are chosen sufficiently. Attention is paid to the tuning required in order to set the equilibrium point at a position which is arbitrarily close to having quasi-zero stiffness while avoiding issues arising from mechanical instability.