Modelling of spatial variations in vibration analysis with application to an automotive windshield

This paper concerns the modelling of spatial variations using random fields and the implementation within existing finite element models. In addition, the application of the line-sampling technique to estimate the distribution and statistics of eigenfrequencies is presented, which can drastically reduce numerical costs. In particular, the vibration analysis of an automotive windshield with uncertain parameters is considered. The analysis is based on a finite element model of the baseline system and information about the related parameter uncertainties. The variation in the frequency response of the windshield is investigated for the cases of a free and constrained configuration of the windshield. Spatial variations are considered for the thicknesses of the five layers of the laminate windshield and for the properties of the glue-joint by which the windshield is mounted on the car. First, the theoretical background of random fields is reviewed and the implementation within a standard finite element code is discussed. A Monte Carlo simulation approach is used to estimate the response statistics. Next, a case study is performed to investigate the influence of the random field parameters. Finally, the application of the line-sampling technique to estimate the distribution and statistics of eigenfrequencies is presented.