A stochastic integral formulation for mid- and high- frequency structure-borne investigations

The fundamentals of a new boundary element formulation applied to the study of structural dynamics with applications in the mid- and high- frequencies are proposed in this paper. Random geometrical parameters are introduced to the integral representations in order to model the increasing sensitivity of the harmonic vibrational responses to any parameter perturbation when the frequency increases. It is shown that the significant unknowns of the formulation are the expectations of the square bound- ary kinematic unknowns. Indeed, these variables are able to describe accurately the responses of the structures in the low-frequency field and deliver a smooth response in the high-frequency domain, corresponding to the global trend of the structural dynamic response in this frequency domain. Fi- nally, the mid-frequency domain, defined as the frequency range for which low and high frequency behaviour can be identified at the same time in the response, is treated by introducing the random- ness only on well chosen subsystems of the complete structure. This enables to predict the well seperated peaks generated by the subsystems for which the wave length is in the same order of mag- nitude than the dimensions of the substructure (so-called the low frequency behaving substructure), while the strongly oscillating part of the response due to the high frequency behaving substructure is smoothened.