Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristics

The frequency range over which a linear passive vibration isolator is effective, is often limited by the mount stiffness required to support a static load. This can be improved upon by employing nonlinear mounts incorporating negative stiffness elements configured in such a way that the dynamic stiffness is much less than the static stiffness. Such nonlinear mounts are used widely in practice, but rigorous analysis, and hence a clear understanding of their behaviour is not readily available in the literature. In this paper, a simple system comprising a vertical spring acting in parallel with two oblique springs is studied. It is shown that there is a unique relationship between the geometry and the stiffness of the springs that yields a system with zero dynamic stiffness at the static equilibrium position. The dynamic stiffness increases monotonically with displacement either side of the equilibrium position, and this is least severe when the oblique springs are inclined at an angle between approximately 48° and 57°. Finally, it is shown that the force–displacement characteristic of the system can be approximated by a cubic equation.