A BROAD FREQUENCY VIBRATION ANALYSIS OF BUILT-UP STRUCTURES WITH MODAL UNCERTAINTIES

A Fourier Spectrum Element Method (FSEM) is proposed for the vibration analysis of built-up structures. The basic idea of FSEM is to treat a complex structure as an assembly of a number of fundamental structural components such as beams, plates, and shells. The primary variables, usually the displacements, over each component are sought as a modified Fourier series expansion which is guaranteed to be uniformly convergent at any desired rate for any boundary and coupling conditions. The Fourier coefficients are considered as the generalized coordinates and determined using the Rayleigh-Ritz method. Mathematically, this Fourier series method does not involve any assumption or an introduction of any artificial model parameters, and it is broadly applicable to the whole frequency range which is usually divided into low, mid, and high frequency regions. The mesh-less and grid-free representation of the subsystems makes FSEM particularly attractive and useful for statistical analyses and parametric studies. As an example, this method is used to study the vibration characteristics of a coupled beam-plate structure with uncertain modal parameters. 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.