Progressive phase trends in multi-degree-of-freedom systems

The relative phase of the response of a dynamical system to its excitation has been largely ignored in problems dealing with noise response of such systems. This is because mean-square amplitude functions are able to predict many of the quantitites that one is interested in such as crack growth, noise radiation, and clearance impact probabilities without concern for phase. But phase has an essential role in other cases, such as phase coherence of vibration fields, or the design of filters to ‘‘dereverberate’’ a received signal. This paper describes some early results of the analysis of phase response of multi-degree-of-freedom systems, using ideas that are closely related to statistical energy analysis, until now, used exclusively for the kinds of problems listed above that tend to ignore phase. The present results show good agreement between simple theory and experiments, but more importantly, they suggest directions for further work that should have significant payoff in the future.