Saddle Point Method Interpretation of Transient Processes in Car Tires

The problem of mechanical excitation of a suspended tire is studied experimentally and theoretically. The tire is considered as an elastic waveguide. Its numerical description is provided by the Waveguide Finite Element Method (WFEM). A case of tire excitation by a δ-shaped pulse is considered, which corresponds to a short kick applied to some point of the tire. The paper focuses on asymptotic analysis of the formal solution. Mainly, a forerunner is evaluated, which is a fast non-stationary wave having an exponential decay. A modification of the saddle point method, namely, a multi-contour saddle point method, is applied for such an estimation. In the framework of this method, we look for the saddle points of the analytical continuation of the dispersion diagram of the waveguide, taking into account that the contours of integration form a family of curves on the dispersion diagram. The tire pulse response is also measured experimentally. A good agreement between the experimentally observed forerunner and its theoretical prediction is shown.