An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires

Abstract

The transient dynamic response of rolling tires is of essential importance for comfort questions, e.g. noise radiation. Whereas finite element models are well established for stationary rolling simulations, it lacks computational methods for the treatment of the high frequency response. One challenge is the large mode density of tire structures that is up to the acoustic frequency domain and another lies on the physically correct description of rolling (gyroscopic) structures. Despite that the eigenvalue analysis of gyroscopic systems, described by complex-valued quadratic eigenvalue systems, seems to be well understood in general, specific problems arise for the computability of large scale three-dimensional tire models. In this presentation an overall computational strategy for the high frequency response of FE-tire models is outlined, where special emphasis is placed upon the efficient numerical treatment of the complex-valued eigenproblems for large scale gyroscopic systems. The practicability of the proposed approach will be demonstrated by the analysis of detailed finite element tire models. The physical interpretation of the computational results is also discussed in detail.