Observations of nonlinear eigen-states, localized versus non-imaging modal response of contact structures

In scientific inquiry of small scale energy and transition events, the effect of an observer on the measurement can be substantial. Similarly, the methods of observation can create entirely different understandings of the system behavior, discussed here on a macro scale. An example using laser vibrometry analysis of nonlinear clattering contact of armor plate shows the difference between the common measurement-at-a-point compared to measuring the system dynamics from the simultaneous behavior of the entire structure which can be useful for remote identification of these ground and air vehicles. The former pencil-thin laser technique fits the keep-it-simple maxim but hides crucial coupling data. With careful observation methods it is possible to measure the structural modal frequencies and calculate the transition probabilities between these discrete modes. This work shows the genesis of what is sometimes called 1/f "noise" which is explained by Zienkiewicz and shown by analysis and simulation herein - that the energy of the essentially discrete structural vibration modes decreases with increasing mode number (and frequency).