## 5pSA5. Fuzzy structure mass per unit frequency and its asymptotic tendencies.

### Session: Friday Afternoon, May 17

### Time: 3:05

**Author: Allan D. Pierce**

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

**Abstract:**

The fuzzy structure theory concept of modal mass per unit natural frequency
is explored for an elastic substructure attached to a master structure. The
passive influence on the master structure vibration is specified by the driving
point impedance of the substructure, which in turn is expressed as a sum over
terms, each corresponding to a natural mode. Term parameters are a modal mass in
the numerator and the natural frequency. The fuzzy structure idealization
replaces the sum by a derivative term (dissipative part) plus an integral
(reactive part), both involving modal mass per unit frequency. Generic continuum
models of the attachment are inhomogeneous rods, beams, and plates. (In the
latter cases, the impedance becomes a matrix, with generalized forces
incorporated that correspond to torques, and generalized velocities that are
angular velocities.) Asymptotic ideas analogous to those that yield modal
density predictions yield predictions of the mass per unit natural frequency
(and its generalizations) in the limit of high frequencies. [Work supported by
ONR.]

from ASA 131st Meeting, Indianapolis, May 1996