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Shock and Vibration
Volume 15, Issue 3-4, Pages 383-393

Simple Models for the Dynamic Modeling of Rotating Tires

J.C. Delamotte, R.F. Nascimento, and J.R.F. Arruda

Departamento de Mecânica Computacional, Universidade Estadual de Campinas, Rua Mendeleiev, s/n, Cidade Universitária “Zeferino Vaz”, 13.083-970, Campinas, SP, Brazil

Received 29 April 2008; Revised 29 April 2008

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Large Finite Element (FE) models of tires are currently used to predict low frequency behavior and to obtain dynamic model coefficients used in multi-body models for riding and comfort. However, to predict higher frequency behavior, which may explain irregular wear, critical rotating speeds and noise radiation, FE models are not practical. Detailed FE models are not adequate for optimization and uncertainty predictions either, as in such applications the dynamic solution must be computed a number of times. Therefore, there is a need for simpler models that can capture the physics of the tire and be used to compute the dynamic response with a low computational cost. In this paper, the spectral (or continuous) element approach is used to derive such a model. A circular beam spectral element that takes into account the string effect is derived, and a method to simulate the response to a rotating force is implemented in the frequency domain. The behavior of a circular ring under different internal pressures is investigated using modal and frequency/wavenumber representations. Experimental results obtained with a real untreaded truck tire are presented and qualitatively compared with the simple model predictions with good agreement. No attempt is made to obtain equivalent parameters for the simple model from the real tire results. On the other hand, the simple model fails to represent the correct variation of the quotient of the natural frequency by the number of circumferential wavelengths with the mode count. Nevertheless, some important features of the real tire dynamic behavior, such as the generation of standing waves and part of the frequency/wavenumber behavior, can be investigated using the proposed simplified model.