Research Papers

Determining the Power Flow in a Rectangular Plate Using a Generalized Two-Step Regressive Discrete Fourier Series

[+] Author and Article Information
Cedric Vuye

Associate Professor
Department Of Industrial Sciences,
Artesis University College,
Paardenmarkt 92,
2000 Antwerp, Belgium
e-mail: cedric.vuye@artesis.be

Patrick Guillaume

e-mail: patrick.guillaume@vub.ac.be

Steve Vanlanduit

e-mail: steve.vanlanduit@vub.ac.be

Flavio Presezniak

e-mail: fpresezniak@gmail.com

Gunther Steenackers

e-mail: gunther.steenackers@artesis.be
Acoustics and Vibration Research Group,
Department Of Mechanical Engineering,
Vrije Universiteit Brussel,
Pleinlaan 2,
1050 Brussels, Belgium

1Corresponding author.

2Currently employed as Professor at Artesis University College.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 1, 2009; final manuscript received March 14, 2012; published online October 29, 2012. Assoc. Editor: Stephen A. Hambric.

J. Vib. Acoust 134(6), 061007 (Oct 29, 2012) (9 pages) doi:10.1115/1.4006756 History: Received October 01, 2009; Revised March 14, 2012

The evaluation of structural power flow (or structural intensity (SI)) in engineering structures is a field of increasing interest in connection with vibration analysis and noise control. In contrast to classical techniques such as modal analysis, the SI indicates the magnitude and direction of the vibratory energy traveling in the structures, which yields information about the positions of the sources/sinks, along with the energy transmission path. In this paper, a new algorithm is proposed to model operational deflection shapes (ODS). The model is a two-dimensional Fourier domain model that is estimated by using a weighted nonlinear least-squares method. From the wave number-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. The proposed method is less sensitive to measurement noise than traditional power flow estimation techniques. A numerical model of a simply supported plate excited by two shakers, phased to act as an energy source and sink, is used as a simulation case. Measurements are executed on a clamped plate excited by an electromagnetic shaker in combination with a damper.

Copyright © 2012 by ASME
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Fig. 1

Flow chart of the G2RDFS

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Fig. 2

Absolute value of the simulated mode shape at 69 Hz

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Fig. 3

(a) Maximum likelihood estimated FFT results, and (b) stabilization chart for the x- direction. Legend: * unstable pole; ♦ stable damping; × stable frequency; ⋆ stable pole.

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Fig. 4

Absolute value of the simulated ODS at 311 Hz

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Fig. 5

Stabilization chart for the simulated test case without added noise. Legend: * unstable pole; ◊ stable damping; × stable frequency; - ⋆ stable pole.

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Fig. 6

Power flow for the simulated test case at 311 Hz using different formulations

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Fig. 7

Divergence of the power flow for the simulated test case at 311 Hz using different formulations

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Fig. 8

G2RDFS: Power flow and divergence for the simulated test case with 5% added noise at 311 Hz

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Fig. 9

Overview of the measurement setup: (a) excitation point, and (b) rubber damper

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Fig. 10

Power flow and divergence for the clamped plate with a rubber damper at 615 Hz



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