Affiliations: Laboratoire de Tribologie et Dynamique des Syst\`emes
UMR-CNRS 5513, Ecole Centrale de Lyon, Ecully Cedex, France | EADS Innovation Works, Suresnes, France
Note: [] Corresponding author: Jean-Jacques Sinou, Laboratoire de
Tribologie et Dynamique des Systèmes UMR-CNRS 5513, Ecole Centrale de
Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France. E-mail:
jean-jacques.sinou@ec-lyon.fr
Abstract: 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.
