A Simpler Formulation for Effective Mass Calculated from Experimental Free Mode Shapes of a Test Article on a Fixture

Abstract

Effective mass for a particular mode in a particular direction is classically calculated using a combination of fixed base mode shapes, the mass matrix, and a rigid body mode shape from a finite element model. Recently, an experimental method was developed to calculate effective mass using free experimental mode shapes of a structure on a fixture (the base) along with the measured mass of the fixture and of the test article. The method required three steps. The first step involved constraining all the free modes of the fixture except one rigid body mode in the direction of interest. The second step involved calculating pseudo-modal participation factors for this case. The third step involved constraining the final fixture rigid body degree of freedom and utilizing the constraint matrices with pseudo-modal participation factors to obtain the estimate of the standard modal participation factors which can be converted to effective mass. This work provides a simpler formulation. After the constraint in step one above, the effective masses are calculated directly from the mass normalized mode shapes of the fixture. In most cases this method gives the same answer as the original approach, within experimental error. In some instances, it appears more robust with low signal to noise ratios. It also provides better physical insight as to which modes have significant effective mass in a particular direction. The new approach is illustrated by experimental example.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy National Nuclear Security Administration under Contract DE-AC04-94AL85000.