| Mathematical models for the force-displacement response of elastomeric bushings are considered for two one-dimensional modes of motions, axial and torsional, and for a coupled mode, axial-torsional response. Two levels of mathematical models were considered. The first model is an exact formulation in the context of continuum mechanics, and consists of the field equations and a three-dimensional nonlinear single integral constitutive equation for nonlinear viscoelastic response of the bushing material. The force-displacement relation is implicit and requires the solution of a nonlinear Volterra integral equation governing spatial variation of relevant quantities. This involves expensive computation. The second model is an assumed explicit form for the force-displacement relation which incorporates nonlinear viscoelastic response. This model is intended to be an approximation to the exact model.;The exact model is solved numerically for specific motions in the axial, torsional, and coupled axial-torsional modes of response. These numerical solutions are regarded as numerically generated experimental data, and are used to determine the relevant properties in the approximate model. In the case of one-dimensional response, these properties are determined by a previously defined extrapolation process. In the case of coupled response, the specific motions are used to determine the mathematical form which accounts for coupling in the material properties. The exact model and the approximate model are used to compute the response of the bushing to a number of displacement histories, for the purpose of comparison. It is found that there is good agreement between the predictions of the models within a reasonable time interval. |
