## 5pSA7. Response of a fuzzy structure in terms of the impulse response function.

G. Maidanik

J. Dickey

CD/NSWC, Code 703, Bethesda, MD 20084

A master structure is defined in terms of a known and proper impulse response function g[sub (infinity)](x|x',(omega)), where x is the spatial variable that spans the master structure and (omega) is the frequency variable. The response v[sub (infinity)](x,(omega)) of the master structure to the external drive p[sub e](x,(omega)) is stated in the form v[sub (infinity)](x,(omega))=(integral)g[sub (infinity)](x|x',(omega))dx' p[sub e](x',(omega)), where dx is an elemental ``volume'' in the x domain. An ensemble of appendages is attached to the master structure. The ensemble and its attachment configures an appended master structure. The response v(x,(omega)) of the appended master structure is stated in the form v(x,(omega))=(integral)g[sub (infinity)S](x|x',(omega))dx' p[sub e](x ',(omega)), where g[sub (infinity)S](x|x',(omega)) is the impulse response function of the appended master structure and it is assumed that the external drive remains unchanged. In the preceding equation it is implied that g[sub (infinity)S](x|x',(omega)) is properly derived; indeed, without this propriety the equation is meaningless. An ensemble of configurations defines a master structure that is variously appendaged. When the ensemble of configurations is statisticalized, a fuzzy structure is defined. Using this equation and designating statistical averaging over configurations by angular brackets, one obtains the response of a fuzzy structure in the form =(integral)dx' p[sub e](x',(omega)). In only statistical variations in the properties of the appendages and their attachments are involved; a proper g[sub (infinity)S](x|x',(omega)) is not committed to v(x,(omega)) and p[sub e](x,(omega)). Thus it is argued that the last equation is an acceptable solution to the response of a fuzzy structure.