Allan D. Pierce
Dept. of Aerosp. and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215
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.