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Research Papers

An Experimental Investigation of State-Variable Modal Decomposition for Modal Analysis

[+] Author and Article Information
Umar Farooq

 Dynamics and Vibrations Research Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824farooqu1@egr.msu.edu

Brian F. Feeny1

Department of Mechanical Engineering,  Michigan State University, East Lansing, MI 48824feeny@egr.msu.edu

1

Corresponding author.

J. Vib. Acoust 134(2), 021017 (Jan 26, 2012) (8 pages) doi:10.1115/1.4003156 History: Received December 18, 2009; Revised April 07, 2010; Published January 26, 2012; Online January 26, 2012

This work presents the experimental evaluation of the state-variable modal decomposition method for a modal parameter estimation of multidegree-of-freedom and continuous vibration systems. Using output response ensembles only, the generalized eigenvalue problem is formed to estimate eigenfrequencies and modal vectors for a lightly damped linear clamped-free experimental beam. The estimated frequencies and modal vectors are compared against the theoretical system frequencies and modal vectors. Satisfactory results are obtained for estimating both system frequencies and modal vectors for the first five modes. To validate the actual modes from the spurious ones, modal coordinates are employed, which, together with frequency and vector estimates, substantiate the true modes. This paper also addresses the error associated with estimation when the number of sensors is less than the active/dominant modes of the system shown via a numerical example.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The experimental setup of a clamped-free beam sensed with 16 accelerometers

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Figure 2

Superposed snapshots of the 16 acceleration sample values, connected by lines across the clamped-free beam

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Figure 9

SVMD is compared for the fifth beam mode against the theoretical mode for N=1000 samples. SVMD is shown with the + symbols, and the theoretical mode is shown with the solid line.

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Figure 3

The amplitude plot of the FFT of the clamped-free beam. Only the first six modes are represented

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Figure 4

The frequency response of the second order high-pass filter for the post processing of the sensor signals

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Figure 5

SVMD is compared for the first beam mode against the theoretical mode for N=1000 samples. SVMD is shown with the + symbols, and the theoretical mode is shown with the solid line.

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Figure 6

SVMD is compared for the second beam mode against the theoretical mode for N=1000 samples. SVMD is shown with the + symbols, and the theoretical mode is shown with the solid line.

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Figure 7

SVMD is compared for the third beam mode against the theoretical mode for N=1000 samples. SVMD is shown with the + symbols, and the theoretical mode is shown with the solid line.

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Figure 8

SVMD is compared for the fourth beam mode against the theoretical mode for N=1000 samples. SVMD is shown with the + symbols, and the theoretical mode is shown with the solid line.

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Figure 10

SVMD modal coordinates are shown for the first five beam modes based on N=1000 sample points. Modal coordinates indicate the quality of the decomposition and can be used to distinguish between spurious and true modes.

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Figure 11

SVMD modal coordinates are shown for the third beam mode based on N=1000 samples. Modal coordinates can be used to distinguish between spurious and true modes. The true modal coordinate is shown in the solid line, whereas the spurious coordinate is shown in the dashed line.

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