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Shock and Vibration
Volume 4, Issue 4, Pages 231-239

Comparison of Force Reconstruction Methods for a Lumped Mass Beam

Vesta I. Bateman, Randall L. Mayes, and Thomas G. Carne

Sandia National Laboratories, Albuquerque, NM 87185-0555, USA

Revised 4 February 1994

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two extensions of the force reconstruction method, the sum of weighted accelerations technique (SWAT), are presented in this article. SWAT requires the use of the structure’s elastic mode shapes for reconstruction of the applied force. Although based on the same theory, the two new techniques do not rely on mode shapes to reconstruct the applied force and may be applied to structures whose mode shapes are not available. One technique uses the measured force and acceleration responses with the rigid body mode shapes to calculate the scalar weighting vector, so the technique is called SWAT-CAL (SWAT using a calibrated force input). The second technique uses the free-decay time response of the structure with the rigid body mode shapes to calculate the scalar weighting vector and is called SWAT-TEEM (SWAT using time eliminated elastic modes). All three methods are used to reconstruct forces for a simple structure.