A study to determine the effect of artificial tangential inertia on the dynamic response of elastic rings.
Hickman, Harold William
Ball, Robert E.
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The elastic transient response of an impulsively loaded circular ring is examined. The numerical stability criterion associated with a finite difference formulation of the problem is briefly discussed, and a method to reduce the stability restriction is presented. This method assumes that the density of the ring is greater in the tangential direction than it is in the radial direction. The analytical solution to the ring equations with the artificial tangential inertia is determined for a specific impulsive load. This solution is compared with the solution to the ring equations with the correct tangential inertia. The comparison shows that on the basis of predicting peak values of stress, the results for the ring with the artificial tangential inertia are very close to those of the unmodified ring. Thus, the method reduces the numerical stability requirements and does not significantly affect the principal results.
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