Abstract
The frequency domain of many problems in structural dynamics encompasses a wide range, covering nearly static behavior up to vibration flow characteristics similar to heat transfer. This work presents an uniform approach for low and high frequency vibration analysis, which is based on Finite Element modeling of the structure. Vibrations in the low frequency range are determined by an efficient superposition technique of complex modes, which accounts accurately for any linear damping effect. The modal method is extended to the high frequency domain by applying different levels of averaging to the response and eigenfrequencies and by the introduction of random properties of modeshapes. The high frequency domain is defined by the size of the Finite Elements, i.e. short wave lengths of high frequency modeshapes cannot be represented by the FE-model. The response computation of isolated structures is extended to substructures of complex systems by prescribing stochastic multi-support base excitation at the substructure boundaries. It may be noted, that the presented approach of stochastic high frequency dynamics contains, as special cases, the expressions of the structural response of Statistical Energy Analysis, Bolotin’s integral method and the results of Asymptotic Modal Analysis.
