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

## 5pSA1. An asymptotic analysis of the added damping effect of a
distribution of fuzzy attachments with steady state excitation.

**Daniel A. Russell
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Victor W. Sparrow
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*Graduate Prog. in Acoust., Penn State Univ., University Park, PA 16802
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In the current state of fuzzy structure theory, it is recognized that the
primary effects of a fuzzy substructure are a frequency-dependent effect added
damping and a frequency-dependent effective added mass. In this paper the fuzzy
substructure is modeled, in accordance with current practice, as a system of
independent 1-DOF oscillators whose masses are distributed with respect to
natural frequency. The exact form of the distribution is shown to be relatively
unimportant as long as it is smooth and continuous. The effects of the system
of attachments, in response to steady-state excitation of the master structure
to which they are attached, are obtained through an analysis of the input
mechanical impedance. The real part of this impedance represents the effective
added damping. Two asymptotic limits are investigated. In the first limit, the
number of attachments becomes very large (N->(infinity)), and the impedance sum
approaches an asymptotic integral. In the second limit, the damping ratio of
the attachments becomes very small ((zeta)->0), and the asymptotic integral
reduces to a simple algebraic expression. Comparison of the impedance sum and
the asymptotic expression, in light of the product N(zeta), suggests that the
simple asymptotic expression is valid for steady-state excitation, as long as
(zeta)(less than or approximately equal to)0.01, and the product
N(zeta)(greater than or approximately equal to)2. [Work supported by ONR.]