Modeling the Vibrations of and Energy Distributions in Car Body Structures 2011-01-1573

A general numerical method, the so-called Fourier Spectral Element Method (FSEM), is described for the dynamic analysis of complex systems such as car body structures. In this method, a complex dynamic system is viewed as an assembly of a number of fundamental structural components such as beams, plates, and shells. Over each structural component, the basic solution variables (typically, the displacements) are sought as a continuous function in the form of an improved Fourier series expansion which is mathematically guaranteed to converge absolutely and uniformly over the solution domain of interest. Accordingly, the Fourier coefficients are considered as the generalized coordinates and determined using the powerful Rayleigh-Ritz method. Since this method does not involve any assumption or an introduction of any artificial model parameters, it is broadly applicable to the whole frequency range which is usually divided into low, mid, and high frequency regions. Further, because the current model is mesh-less and grid-free, it is particularly suited for sensitivity and statistical analyses and facilitates a smooth transition between the different frequency regions by switching on/off any statistical processing or spatial- and frequency-averaging features. As an example, this method is used to study the vibration characteristics of a car body structure (body-in-white). It is shown that the spatial- and frequency-averaging processes may not be desired for the mid-frequency analysis because the important dynamic characteristic of a system tends to be completely wiped out by them.