An experimental exploration of the properties of random frequency response functions

The vibro-acoustic analysis of complex structures over a broadband frequency range is an extremely challenging problem that may often require the use of a hybrid deterministic-statistical approach. Due to manufacturing imperfections, the frequency response functions (FRFs) of an ensemble of nominally identical systems can be considered to be random. These FRFs, however, have statistical properties that can be potentially used in vibro-acoustic models. This work explores some of these fundamental properties by using measured FRFs from an ensemble of nominally identical structures, obtained by randomising a thin rectangular plate using point masses. It is first shown that the measured ensemble of FRFs satisfies the analyticity-ergodicity condition, experimentally verifying this recently demonstrated fundamental property. Then, the ensemble is used to explore whether the direct field dynamic stiffness, a key parameter in a well-established hybrid deterministic-statistical formulation, can be obtained experimentally. The results are compared against those computed using numerical techniques, showing that measured data may be a suitable alternative provided that an ensemble of systems can be measured. Finally, an alternative method, based on the use of virtual point masses, opposed to physical ones, is proposed for those cases where experimental randomisation is particularly challenging. It has been found, however, that the method may be extremely sensitive to measurement imprecisions, specially when applied to lightly damped structures. It is concluded that the statistical properties of random causal FRFs are not only interesting in themselves, but can enhance and extend vibro-acoustic prediction models