### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 4aSA2. Fuzzy elements, their coupling rules, and the Jaynes--Shannon
maximum entropy principle.

**Allan D. Pierce
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*Boston Univ., Dept. of Aerospace and Mech. Eng., 110 Cummington St.,
Boston, MA 02215
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Emerging theories of fuzzy structures are regarded as the wholesale
replacement of certain portions of the structure by fuzzy elements, whose chief
characteristic is a smeared-out (fuzzied) distribution of natural frequencies,
so that there are an infinite number of natural frequencies in any given
frequency band. Descriptors of fuzzy elements are the mass per unit natural
frequency band and the elements of a mass matrix per unit natural frequency
band. Modeling of complex structures is simplified by regarding internal and
appended structures as assemblages of coupled fuzzy elements, so circuit laws
are here suggested for determining parameters of an overall fuzzy element from
the known features of its fuzzy components. In regard to assigning mass
distributions among frequencies to actual elements that are to be modeled as
fuzzy elements, the appropriate guide is Jaynes's (1957) general method of
statistical inference (principle of maximum entropy) extracted from Shannon's
information theory. The mass distribution is regarded as a probability
distribution, and the known features, such as total mass, asymptotic behavior,
mass-weighted average natural frequency, d-c behavior, are imposed as
constraints on a variational principle that maximizes the entropy asssociated
with that probability distribution, to find the most likely such distribution
consistent with the known information. [Work supported by Office of Naval
Research.]