A radial automobile tire undergoing steady‐state rotation is analyzed by a finite element method. A special formulation is used which allows the finite element equations to be solved as a quasi‐static problem using static analysis solution procedures, rather than as a dynamic problem requiring solution in the time domain. This is accomplished through a transformation of variable that changes time derivatives, present through inertia, to spatial derivatives. Solution time for the analysis is thereby shortened.

The tire is modeled first as a two‐dimensional ring on an elastic foundation, then in its full three‐dimensional geometry. Rotational speeds are those at which resonance occurs so that the dynamics can be easily visualized and the response easily verified. The models are subjected to point load excitation or ground contact. Point load is used to predict resonance responses of the undamped tire. Results agreed well with experimental measurements. The effect of inertia components and damping on vibrational response of the tire was studied by imposing ground contact at one of the resonance speeds. Damping is included in the model through a two‐element Kelvin‐Voight viscoelastic material model. Responses of the models were similar to standing wave deformations in a tire.

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