Simulation of Payne effect of elastomeric isolators with a harmonic balance method

In the presented work, a non linear effect of rubber referred as Fletcher-Gent effect or Payne effect is investigated. It leads to a change in the rubber dynamic modulus with vibration amplitudes and, consequently, modifies resonance frequencies of mechanical systems including non linear elastomers. In this study a new methodology is developed to take into account Payne effect in a linear viscoelastic rubber material. Small vibration amplitudes around a no-preloaded state are predicted by considering frequency and amplitude dependencies of the material. This methodology has the advantage of using tabular experimental data from characterization tests which avoids the development of a complex model. In order to compute frequency responses, the non linear harmonic balance method is used and, for each iteration, new rubber properties are affected at each element according to its strain state. An equivalent strain measure is evaluated from the element strain energy density. This equivalent strain allows to associate dynamic properties of a material element subjected to multiaxial strain state with experimental dynamic properties of a material sample subjected to an uniaxial strain state. Practically, DMAP alter procedures are developed in order to evaluate energies in models defined with MSC.Nastran and the non linear solver is developed with Matlab. The method is applied on a satellite instrument isolator including four non linear rubber mounts. A non homogeneous spatial distribution of element equivalent strains is observed. Moreover, the maximum equivalent strain varies with frequency. These two observations validate the use of a specific methodology to deal with amplitude dependency of rubber.