In many applications of vibration technology, especially in chassis, air springs present a common alternative to steel spring concepts. A design-independent and therefore universal approach is presented to describe the dynamic characteristic of such springs. Differential and constitutive equations based on energy balances of the enclosed volume and the mountings are given to describe the nonlinear and dynamic characteristics. Therefore all parameters can be estimated directly from physical and geometrical properties, without parameter fitting. The numerically solved equations fit very well to measurements of a passenger car air spring. In a second step a simplification of this model leads to a pure mechanical equation. While in principle the same parameters are used, just an empirical correction of the effective heat transfer coefficient is needed to handle some simplification on this topic. Finally, a linearization of this equation leads to an analogous mechanical model that can be assembled from two common spring-and one dashpot elements in a specific arrangement. This transfer into "mechanical language" enables a system description with a simple force-displacement law and a consideration of the nonobvious hysteresis and stiffness increase of an air spring from a mechanical point of view.

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Modelling the viscoelastic behaviour of rubber for use in component design remains a challenge. Previous reviews (Diani, Fayolle, & Gilormini 2009) and our studies presented in this paper highlight the issues of using of the most common viscoelastic non-linear constitutive models (Besdo & Ihlemann 2003;Bergström & Boyce 1998;Ogden & Roxburgh 1999). In detail, such models cannot reproduce or predict the experimental stress data for filled natural rubber loaded under the typical operating conditions. Examples of such conditions include cyclic strain history with constant strain rates and variable amplitude. This paper examines the behaviour of natural rubber elastomers filled with different percentages of carbon black. The elastomers chosen are typical of the materials used in vibration damping or automotive suspensions. We show that a constitutive model based on the fractional calculus can provide a good agreement for cyclic uniaxial tensile tests at a constant amplitude. The proposed model can capture, for example, the hysteresis and cyclic stress softening observed in the experimental data.