Daniel A. Russell
Victor W. Sparrow
Graduate Prog. in Acoust., Penn State Univ., University Park, PA 16802
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.]