### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2aSA1. Mass per unit natural frequency as a descriptor of internal fuzzy
structure.

**Allan D. Pierce
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*Dept. of Aerosp. and Mech. Eng., Boston Univ., 110 Cummington St., Boston,
MA 02215
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Previous work by the author with Sparrow and Russell, and by Strasberg and
Feit, has suggested that internal mass per unit natural frequency is the
appropriate prime descriptor of the internal structure of a complex system
enclosed by a shell. In the simplest idealization one conceives of many
one-degree-of-freedom (dof) spring-mass systems, coupled only through the outer
shell, and which are attached at random points on the interior surface of the
shell, and one specifies for any small area just how much suspended mass is
associated with a narrow band of natural frequencies. The assumption of large
numbers allows the use of an idealized limit of mass per unit natural frequency
per unit area. The present paper shows from basic principles that this concept
still applies when the individual attachments have multi-dof complexity. The
question is then addressed of how one can deduce this mass-frequency density
when the internal structure is largely a priori unknown (fuzzy internal
structure). A possibility is the sampling of the impedance presented to small
surface areas of the outer shell by the internal structure. Algorithms for
processing the (complex) impedance versus frequency curves yield estimates of
the required information.