### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 4aSA6. Determination of modal masses from plots of driving point impedance
magnitude versus frequency when modal overlap is present.

**Jacques Livingston
**

**
Allan D. Pierce
**

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

*
*
Implementation of a piecemeal technique for the modeling of complex
structures within the context of the theory of fuzzy structures requires that
one have some prior knowledge of the distribution of modal masses for each class
of internal appendages that have similar design features and function. For each
such category, sample calculations or measurements can yield data that can be
gathered into an ensemble and then used in the computational replacement of each
appendage within that category by a generic fuzzy element. The present paper is
concerned with how such data might be obtained from experimental tests that
determine how the magnitude squared of the driving point impedance varies with
frequency. For a lightly damped one-degree-of-freedom system, basic vibration
theory leads to an expression for the (modal) mass which is proportional to the
height of the resonance peak divided by the square root of the magnitude of the
second derivative at that peak. However, for a multidegree-of-freedom or
continuum structure, a fundamental scheme based on the measurement of heights of
peaks and of the second derivatives at such peaks can be frustrated by the
occurrence of strong modal overlap. A numerical iteration method that can
largely overcome this makes use of a general functional form for the complex
impedance and proceeds to gradually ``filter out'' the contributions from the
stronger peaks, so that the weaker peaks can be identified and then also
filtered out. [Work supported by Office of Naval Research.]