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Research Papers

Two Algorithms for Mass Normalizing Mode Shapes From Impact Excited Continuous-Scan Laser Doppler Vibrometry

[+] Author and Article Information
Shifei Yang, Michael W. Sracic

Department of Engineering Physics,  University of Wisconsin-Madison, 0535 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706

Matthew S. Allen

Department of Engineering Physics,  University of Wisconsin-Madison, 0535 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706msallen@engr.wisc.edu

J. Vib. Acoust 134(2), 021004 (Jan 13, 2012) (8 pages) doi:10.1115/1.4005020 History: Received June 04, 2010; Revised July 06, 2011; Published January 13, 2012; Online January 13, 2012

Continuous-scan laser Doppler vibrometry (CSLDV), a concept where a vibrometer measures the motion of a structure as the laser measurement point sweeps over the structure, has proven to be an effective method for rapidly obtaining mode shape measurements with very high spatial detail using a completely non-contact approach. Existing CSLDV methods obtain only the operating shapes or arbitrarily scaled modes of a structure, but the mass-normalized modes are sought in many applications; for example, when the experimental modal model is to be used for substructuring predictions or to predict the effect of structural modifications. This paper extends an approach based on impact excitation and CSLDV, presenting a new least squares algorithm that can be used to estimate the mass-normalized modes of a structure from CSLDV measurements. Two formulations are derived: one based on real-modes that is appropriate when the structure is proportionally damped and a second that accommodates a complex-mode description. The latter approach also gives the algorithm further latitude to accommodate time-synchronization errors in the data acquisition system. The method is demonstrated on a free-free beam, where both CSLDV and a conventional test using an accelerometer and a roving-hammer are used to find its first seven mass normalized modes. The scale factors produced by both methods are found to agree with a tuned analytical model for the beam to within about ten percent. The results are further verified by attaching a small mass to the beam and using the model to predict the change in the structure’s natural frequencies and mode shapes due to the added mass.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic and dimensions of test setup

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Figure 2

Expanded view of CSLDV signal of beam with accelerometer attached

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Figure 3

Complex Mode Indicator Function (CMIF) of CSLDV data after processing by MDTS method. Labels are also shown giving the unaliased natural frequency of the mode that is manifest at each peak.

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Figure 4

Mode shapes for free-free beam with an accelerometer attached at x = 6.4 mm. Solid black lines denote the analytical shapes estimated by Ritz method, dots show the CSLDV shapes at each pseudomeasurement point, and triangles give the results of a hammer - accelerometer test.

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Figure 5

Mode shapes for the free-free beam with an accelerometer at 6.4 mm and a mass added at 246 mm. Solid black lines denote the analytical shapes estimated by Ritz method, dots show the CSLDV shapes at each pseudo-measurement point, and triangles give the results of the hammer-accelerometer test.

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