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Shock and Vibration
Volume 7, Issue 5, Pages 299-308

Analyzing the Total Structural Intensity in Beams Using a Homodyne Laser Doppler Vibrometer

Agnaldo A. Freschi,1 Allan K.A. Pereira,1 Khaled M. Ahmida,1 Jaime Frejlich,2 and José Roberto F. Arruda1

1Departamento de Mecanica Computacional, FEM, Universidade Estadual de Campinas C.P. 6122, Campinas, SP, 13083-970, Brazil
2Laboratório de Óptica, IFGW, Universidade Estadual de Campinas, Brazil

Received 11 June 1999; Revised 26 June 2000

Copyright © 2000 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 total structural intensity in beams can be considered as composed of three types of waves: bending, longitudinal, and torsional. In passive and active control applications, it is useful to separate each of these components in order to evaluate their contribution to the total structural power flowing through the beam. In this paper, a twisted z-shaped beam is used in order to allow the three types of waves to propagate. The contributions of the structural intensity, due to these waves, are computed from measurements taken over the surface of the beam with a simple homodyne interferometric laser vibrometer. The optical sensor incorporates some polarizing optics, additional to a Michelson type interferometer, to generate two optical signals in quadrature, which are processed to display velocities and/or displacements. This optical processing scheme is used to remove the directional ambiguity from the velocity measurement and allows nearly all back-scattered light collected from the object to be detect. This paper investigates the performance of the laser vibrometer in the estimation of the different wave components. The results are validated by comparing the total structural intensity computed from the laser measurements, with the measured input power. Results computed from measurements using PVDF sensors are also shown, and compared with the non-intrusive laser measurements.