Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Automotive Engineering

Committee Chair/Advisor

Ayalew, Beshah

Committee Member

Filipi, Zoran

Committee Member

Pisu, Pierluigi

Committee Member

Rhyne, Timothy


A deformable Ring on Elastic Foundation (REF) model has been widely used for modeling rotating structures such as gears, bearings and tires. This dissertation extends the existing work with three main contributions focusing on applications to tires: 1) The elastic foundation is endowed with unilateral stiffness, which leads to a nonlinear deformation dependent stiffness typical of some non-pneumatic tires; 2) The model of the deformable ring is extended from simple Timoshenko rings to a laminated orthotropic ring model, with bending, shear stiffness and extensibility in the internal layer, and transverse stiffness in the external layer; 3) Facilitated by the laminated ring model, a feedback compensation algorithm is proposed for analysis of frictionless contact of the tire with arbitrary uneven surfaces in both static and rolling contact. By starting from first principles, the dissertation derives the equations of motion for the laminated rotating ring on unilateral foundation. Then, it outlines the solutions for the static and dynamic forced responses as well as for the contact response of the laminated ring on both linear and unilateral foundations. An iterative compensation method is then presented to solve the unilateral foundation problem in the spatial domain, and an implicit Newmark scheme is adopted for time domain integration. Linearizations of the rotating laminated ring on unilateral foundation model are also used for modal analysis, and for computing the critical velocities which are important for predicting standing waves. In most cases analyzed, comparisons with alternative finite element analysis (FEA) software solutions showed that the proposed modeling approach gives very similar results with much reduced computational time and avoids the need for extensive FEA oriented pre-processing. As such, the modeling approach and solution methods proposed in this dissertation are ideally suited for rapidly covering the design space for tire designs with the objective to meet ride comfort requirements over various road surfaces.



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