Dynamic Instability of Tires under Asymmetric Loads

Abstract

This paper presents an analytical procedure for predicting instability loads of composite tires using a simplified tire model. The tire is modeled as a closed composite torus with geometric nonlinearities. The equations of motion of the torus are derived using differential geometry, and the Galerkin procedure is used to discretize the spatial domain. The resulting equations are nonlinear ordinary differential equations with constant coefficients. However, the special form of these equations allows their reduction to linear ordinary differential equations with periodic coefficients. The Floquet theory is then used to determine the stability characteristics of these equations under various loads and an impact velocity loading. The torus is studied in two reinforcement configurations and various fiber volume fractions. Both configurations show a threshold value for the applied load at which the stability of the periodic solution is lost in a catastrophic manner. Both reinforcement schemes shows the same optimum value for fiber volume fraction at which the instability load is maximum.