Almost any seismic suspension can b

Almost any seismic suspension can be made astatic by inserting an external force acting normal to the line of mass motion and pushing the mass away from its equilibrium. A theoretical model of a quasi-zero-stiffness isolator is presented in [ Carella2009 ]. Such a system has one vertical spring and oblique ancillary springs, as shown in figure 2.18a. The ancillary springs can be linear, pre-stressed or non-linear. The authors derive the maximum transmissibility under the assumption of light damping and give the so called jump-down frequencies, at which the transmissibility of the non-linear system jumps to a lower value. They show that there are advantages in having non-linear and pre-stressed oblique springs. However, the practical realisation of oblique springs with precise non-linear characteristics is considered difficult. Neither the restoring force of the original suspension nor the ancillary spring force can be made perfectly proportional to the displacement. While linear components of the force may cancel out, the non-linear terms will remain and cause the oscillation to become non-harmonic and even unstable at large amplitudes. Viscous and hysteretic behaviour of the springs would also become noticeable [Wielandt2002].