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

Boston Univ., Dept. of Aerospace and Mech. Eng., 110 Cummington St., Boston, MA 02215

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.]