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Shock and Vibration
Volume 11, Issue 3-4, Pages 333-350

Estimation of the Rotational Terms of the Dynamic Response Matrix

D. Montalvão,1 A.M.R. Ribeiro,2 N.M.M. Maia,2 and J.M.M. Silva2

1Department of Mechanical Engineering, Escola Superior de Tecnologia, Polytechnic Institute of Setúbal Campus do IPS, Estefanilha, 2910-761 Setúbal, Portugal
2Department of Mechanical Engineering, Instituto Superior Técnico, Technical University of Lisbon Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Received 24 August 2004; Revised 24 August 2004

Copyright © 2004 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.


The dynamic response of a structure can be described by both its translational and rotational receptances. The latter ones are frequently not considered because of the difficulties in applying a pure moment excitation or in measuring rotations. However, in general, this implies a reduction up to 75% of the complete model. On the other hand, if a modification includes a rotational inertia, the rotational receptances of the unmodified system are needed. In one method, more commonly found in the literature, a so called T-block is attached to the structure. Then, a force, applied to an arm of the T-block, generates a moment together with a force at the connection point. The T-block also allows for angular displacement measurements. Nevertheless, the results are often not quite satisfactory. In this work, an alternative method based upon coupling techniques is developed, in which rotational receptances are estimated without the need of applying a moment excitation. This is accomplished by introducing a rotational inertia modification when rotating the T-block. The force is then applied in its centroid. Several numerical and experimental examples are discussed so that the methodology can be clearly described. The advantages and limitations are identified within the practical application of the method.