Carrella, Alessandro
(2008)
Passive vibration isolators with high-static-low-dynamic-stiffness.
*University of Southampton, Institute of Sound and Vibration Research, Doctoral Thesis*, 226pp.

## Abstract

In many engineering applications there is need to reduce the level of vibrations that are transmitted from a source to a receiver. Amongst several different techniques, the most commonly adopted solution is to interpose an isolation mount between the source and the receiver. Ideally, a vibration isolation mount would have a high static stiffness to prevent too large a static displacement to occur, but a low dynamic stiffness which reduces the natural frequency and extends the frequency range of isolation. For linear mounts these two features are mutually exclusive. However, an improved compromise can be reached by employing nonlinear mounts. In this thesis the advantages and the limitations of nonlinear isolation mechanisms with a high-static-low-dynamic-stiffness(HSLDS) characteristic are investigated.A study of the static characteristics of two mechanisms with HSLDS is presented. This desired property is obtained by connecting in parallel elements with positive and negative stiffness. For both systems the positive stiffness is given by linear springs. In one model the geometry of the system is exploited to achieve the desired negative stiffness. This is obtained by a pair of linear springs placed at a certain angle to the horizontal (oblique springs). In the second model considered the required negative stiffness is provided by a set of magnets in attracting configuration. In both cases the force and stiffness are approximated to a symmetric cubic polynomial and a quadratic function of the displacement respectively. From a dynamical point of view this allows the system to be treated as a Duffing oscillator. It is argued that for small oscillations about the static equilibrium position the mechanism behaves linearly. A lab-scale rig which reproduces the HSLDS system with magnets and springs is designed and built. The excitation level is chosen to comply with the assumption of small displacement so that the experimental results show that the system responds in a rather linear fashion.The natural frequency of the HSLDS is half that of a linear model with the same static displacement and its transmissibility also compares favourably. A nonlinear analysis is also carried out in order to predict the response of the system when the assumption of linearity no longer holds true. Both cases of harmonic excitation of the payload and of the base are studied. For the two instances an approximate solution to the nonlinear equation of motion is found by applying the method of Harmonic Balance to a first order expansion. The main feature of the dynamic responseof a Duffing oscillator is the jump phenomenon. Herein this is described and analytical expressions for the jump frequencies are also provided. The isolation properties of an HSLDS isolation system are evaluated in terms of the transmissibility and its performance is compared with that of an equivalent linear system. It is shown that the HSLDS has a higher isolation capability.

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