### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

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

**G. Maidanik
**

**
J. Dickey
**

**
**
*CD/NSWC, Code 703, Bethesda, MD 20084
*

*
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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.