Fuzzy structure theory, statistical energy analysis, and resonant-frequency-distribution of internal mass

The present talk gives a historical perspective on two early and relatively little- known papers having to do with fuzzy structure theory. The first is a letter to the editor by Lyon titled “Statistical energy analysis and structural fuzzy” (JASA 1995). The second paper is a slightly later 1997 Journal of Vibrations and Acoustics (ASME) article titled “Resonant-frequency-distribution of internal mass inferred from mechanical impedance matrices, with application to fuzzy structure theory.” The present paper seeks to clarify and qualify Lyon's statement, “It appears hat the fuzzy structure theory of structural interaction is highly compatible with the SEA framework.” The second paper clarifies the concept of modal mass and gives a proof that, for a lightly damped closed mechanical system, you can express the mechanical displacement fiield as a sum of natural modes. With each natural mode, one can associate a fixed amount of mass. The mass, moreover. is additive and sums to the total mass of the system. The idea goes back to some earlier work (1963) of Cunniff and O'Hara of the U. S. Naval Laboratory. The theory leads to the concept of modal mass per unit natural frequency bandwidth, and leads to a justification for the SEA assumption that interactions are between motions of natural modes with comparable natural frequencies.