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.]