# A Hybrid Vibration Isolator Based on Elastomeric and Electromagnetic Restoring Force
## 1 Introduction
In this case, the springs may be sized so that a low stiffness range is reached at the static equilibrium condition with the advantage that the weight involves low displacements thanks to the greater initial stiffness and that, at the equilibrium position, the vertical stiffness (and therefore the vibration transmissibility) is low. Isolators with these characteristics are indicated with the acronym HSLDS (high-static, low-dynamic systems) or QZSS (quasi-zero-stiffness systems) if, in the position of static equilibrium, the stiffness assumes a value of almost zero. [PERSON]'s experience shows that the combination of a negative-stiffness device with a positive one leads to a device with a nonlinear force-displacement relationship and that, if the ratio between the stiffnesses is appropriately chosen, the device can exhibit stability, small static deformation, and high damping ratio as the potential energy produced by a negative stiffness device is negative, which means a loss of energy along with deformation. These characteristics can be conveniently exploited for the mitigation of vibrations. The  
Figure 1: Molyneux spring device: (**a**) scheme; (**b**) force-displacement trend. dynamic behavior of this type of isolator supporting a lumped mass can be approximately described by the Duffing equation [7]. An isolator based on this principle is proposed in [8] to protect structures from vertical seismic accelerations. Low dynamic stiffness isolators have received considerable attention as this isolation technique allows the transmissibility to be reduced by coupling a negative-stiffness device with a positive-stiffness one, as reported in an interesting review in [9]. These devices can be made in different ways, such as by means of inclined springs, buckled beams, and scissor-like mechanisms involving geometric nonlinearities [10]. However, these mechanisms have some drawbacks that limit their application; for example, pre-stressed inclined springs exhibit negative stiffness only when the displacement exceeds a certain limit; buckled beams exhibit an asymmetrical negative stiffness near the equilibrium point; furthermore, they exhibit good performances only close to the nominal operating conditions. Passive isolators are activated by the relative motion between the isolated body and its support; they are preferred to semi-active/active isolators for their simplicity and when it is feared that the external energy contribution may not always be available. Semi-active isolators can be considered passive devices in which it is possible to adjust a rheological property (damping or stiffness) in real time to adapt it to the needs of the isolation. Unlike active systems, they cannot feed energy into the controlled system and are often preferred to active ones as they require less energy and can operate with lower efficiency, even in the absence of external energy. A popular type of semi-active insulator consists of a spring coupled with a magnetorheological damper [11] whose damping can be adjusted in real time. Another type of semi-active isolator is based on the use of magnetorheological rubbers whose properties are shown in [12], and the possibility of controlling their stiffness is explained in [13]. Interesting reviews of this smart material and the possibility of adopting it to realize tunable dynamic vibration absorbers are reported in [14; 15], respectively. Other vibration isolation systems act on different parameters; in [16; 17], the isolation problem is solved by adopting a variable friction device and a switchable stiffener applied to a semi-active pneumatic device, respectively. Among active vibration isolators, some devices, constituted by magnetic springs realized by means of electromagnets or combining permanent magnets with electromagnets, have been proposed. A tuneable device constituted by a mechanical spring in parallel with a magnetic spring composed of two permanent magnets and two electromagnets, is presented in [18].