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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.