known that the difficulty in predicting the response statistics of such structures is immense, due to the complexity of the structure, the large number of variables which might be uncertain, and the inevitable lack of data regarding

the statistical distribution of these variables.

The Symposium participants presented the latest thinking in this very active research area, and novel techniques were presented covering the full frequency spectrum of low, mid, and high frequency vibration problems. It was demonstrated that for high frequency vibrations the response statistics

can saturate and become independent of the detailed distribution of the uncertain system parameters. A number of presentations exploited this physical behaviour by using and extending methods originally developed in both

phenomenological thermodynamics and in the fields of quantum mechanics and random matrix theory.

For low frequency vibrations a number of presentations focussed on parametric uncertainty modelling (for example, probabilistic models, interval analysis, and fuzzy descriptions) and on methods of propagating this uncertainty through a large dynamic model in an effi cient way. At mid frequencies

the problem is mixed, and various hybrid schemes were proposed.

It is clear that a comprehensivesolution to the problem of predicting the vibration response of uncertain structures across the whole frequency range requires expertise across a wide range of areas (including probabilistic and non-probabilistic methods, interval and info-gap analysis, statistical energy analysis, statistical thermodynamics, random wave approaches, and large

scale computations) and this IUTAM symposium presented a unique opportunity to bring together outstanding international experts in these fields.