Flexible polyurethane foams used for cushioning in the furniture and automotive industries serve as foundations and exhibit complex nonlinear viscoelastic behavior. To design systems that incorporate these materials, it is important to model their mechanical behavior and then to predict the dynamic response of such systems. The example of a pinned-pinned beam interacting with a nonlinear viscoelastic foundation is the focus of the present study. The foundation can either react in compression as well as tension (bilateral), or react only in compression (unilateral). In the latter case, the contact regions between the beam and the foundation are not known a priori, and thus the coefficients of the modal equations obtained in a Galerkin approximation solution approach, are functions of the solution as well. It is therefore computationally expensive to predict the dynamic and steady-state response of these structures to static and harmonic loads. For polynomial-type nonlinearities, it is possible to speed up the computation time by using a convolution method to evaluate integral terms in the model. Also, if only the steady-state response is of interest, direct-time integration can be replaced by incremental harmonic balance to make the frequency response predictions more efficient. The effect of axial load and the influence of various parameters e.g., loading configuration, excitation amplitude, linear and nonlinear stiffness, on the response of the beam on unilateral and bilateral foundations are studied.

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