A Fast Method for Computing Convolutions with Structural Green’s Function : Application to Tire/road Contact Problems

Abstract. Tire/road contact represents the major source of traffic noise with driving speed above 50 km/h. One of the most important problems is to take into account the contact conditions and to calculate the contact forces in an accurate way. As a general approach, the dynamic response of the tire is calculated by convolving the contact forces with the Green function of the tire. The disadvantage of this method is that the computation can be time consuming. In this paper, an alternative which is a modal decomposition model is used. The developed method allows quicker calculations than the traditional convolution. It consists, at the first stage, on an approximation of the pre-calculated Green function on a series of modal contributions with the Least Square Complex Exponential (LSCE) algorithm then, on the calculation of the dynamic response in the time domain as a series of SDoF systems response. For verification, the approach is tested by using a Single Degree of Freedom (SDoF) oscillator where the system moves through a sinusoidal road profile with a constant speed. Then, it is applied to the Ring on Elastic Foundation (REF) Model.