Nonlinear viscoelastic behavior is a characteristic of many engineering materials and also biological tissue, yet it is difficult to develop dynamic models of systems that include these materials and are able to predict system behavior over a wide range of excitations. This research is focused on a specific example system in the form of a pinned-pinned beam interacting with polyurethane foam. Two cases are considered: (1) the beam and foam are glued so that they are always in contact and the foam can undergo both stretching and compression, and (2) the beam and foam are not glued so that the contact region changes with beam motion, and the foam only reacts in compression. Static as well as dynamic forces act on the beam and the Galerkin method is used to derive modal amplitude equations for the beam on polyurethane foundation. In the second case, determination of the loss of contact points is integrated into the solution procedure through a constraint relation. The static responses for both cases are examined as a function of the foam nonlinearity and loading conditions, and three and five mode solutions are compared. The steady state response of the system subject to static and harmonic loads is studied by using numerical integration techniques. Numerical challenges and the accuracy of this approach are discussed. Frequency responses are generated for a range of foam nonlinearities and loading conditions.

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