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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.

A rectangular thin-walled box is used as a test problem for comparing the results obtained from finite element analysis (FEA), boundary element analysis (BEA), statistical energy analysis (SEA), and experimental measurement. The box structure is mechanically excited by a random point force generated by a vibration exciter. The structural acoustic coupling has been taken into account because there is a significant acoustical pressure load acting on structural surfaces of the box. Both structural and acoustic responses are investigated and good agreement is observed between the numerical and experimental results.

A frame structure such as vehicle frames is usually the primary load-carrying member and typically plays a dominant role in transmitting vibratory and acoustic energies from excitation sources to a receiver that may be a human body or any other subject sensitive or vulnerable to vibration and noise. Determination of vibratory power flows between beam-like structures has been the subjects of many investigations. However, most of these studies have been confined to some simplified or specific boundary and/or junction conditions. In this investigation, a general analytical method is developed for predicting the vibratory power flows between two beams that are rigidly or non-rigidly coupled together at an arbitrary angle. The cross coupling between the flexural and longitudinal waves at the junction has been taken into account, which becomes necessary when two beams are joined together at an angle.