Date of Award

January 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Anil K. Bajaj

Second Advisor

Patricia Davies

Committee Member 1

James F. Doyle

Committee Member 2

Amit H. Varma

Committee Member 3

Douglas E. Adams


Buildings, railway tracks, drill strings and off-shore pipelines are all modeled as structures on elastic foundations in order to study their response behavior under different conditions. Flexible polyurethane foams used for cushioning in the furniture and automotive industries also serve as foundations, but they exhibit even more complex nonlinear and viscoelastic behavior. It is challenging to develop models that can be used to predict the behavior of these material-structural systems over a wide range of loading conditions. The solution techniques are also computationally expensive, making it difficult to use the models to do iterative design of these types of systems. The research described addresses some of these issues. A pinned-pinned beam interacting with a viscoelastic foundation which can react in tension and compression (bilateral), as well as only in compression (unilateral) is considered. The model developed can be used to predict the response to localized or distributed, static and dynamic forces. If the foundation reacts only in compression, the contact region changes with beam motion and the estimation of the contact region is embedded into the iterative solution procedure. The steady state solution is expressed as the sum of an arbitrary number of modes and Galerkin's method is used to derive the modal amplitude equations. Incremental harmonic balance is used to predict the steady-state frequency responses efficiently. Pseudo arc-length continuation technique is used to track both stable and unstable branches of the response and by using these computationally efficient solution approaches, it is possible to explore a wide variety of static and dynamic loading conditions and also quickly determine the number of modes required for convergence. The influence of various system parameters on the response of the beam on different types of foundations is studied, and the unilateral and bilateral foundation cases are compared. To verify the applicability of the beam-viscoelastic foundation model, an experimental rig was designed and a variety of base excitation experiments were conducted. Predicted and measured responses were compared and additional experiments were conducted to improve estimates of foundation material and beam model. There is a good qualitative agreement between the experimental and predicted responses but a few challenges remain, for example, for more complex foundation models and for viscoelastic materials that take a long time to recover. In these cases the behavior in the end-of-contact regions (unilateral case) may require separate models for the foundation and the beam.