Simulating and Measuring Structural Intensity Fields in Plates Induced by Spatially and Temporally Random Excitation

[+] Author and Article Information
Michael J. Daley

 Akustica, Inc., 2403 Sidney St, Suite 270, Pittsburgh, PA 15203mdaley@akustica.com

Stephen A. Hambric1

Applied Research Laboratory, The Pennsylvania State University, PO Box 30, State College, PA 16804sah@wt.arl.psu.edu

m denotes the mode order along the length of the plate (11.2 cm) and n the mode order along the width (7.5 cm), where the mode order indicates the number of antinodes, or peaks, in the mode shape.

The resonance frequencies of the 12th and 15th modes could not be reliably extracted from the measurements, and are therefore not included in the figure.


Corresponding author.

J. Vib. Acoust 127(5), 451-457 (Jan 06, 2005) (7 pages) doi:10.1115/1.2013299 History: Received August 11, 2004; Revised January 06, 2005

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in flat plates excited by such fields are presented here. The structural intensity at various frequencies in a simply supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives. Specifically, no clear source regions are apparent in the randomly driven intensity fields, although the energy flow patterns do clearly converge toward a point damper attached to the plate.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Free body diagram of differential element of plate

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Figure 2

Diagram of response array used for 13 point finite differencing scheme. S-I vector is computed at center point (point 2).

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Figure 3

Schematic diagram of system used for simulations

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Figure 4

Diagram of plate—dimensions in centimeters

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Figure 5

Photograph of plate, clamped to its massive brass base frame

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Figure 6

Modeled and measured natural frequencies of simply supported plate

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Figure 7

Measured operating deflection shape of plate at (3,1) natural frequency

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Figure 8

Schematic of Point Damper

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Figure 9

Measured and theoretical spatial correlation functions for diffuse acoustic field at the (3,1) resonance frequency of the plate

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Figure 10

Schematic diagram of measurement setup

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Figure 11

Simulated and measured velocity spectra; mode orders for which S-I fields are computed are annotated

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Figure 12

Predicted S-I field at (2,1) resonance frequency

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Figure 13

Measured S-I field at (2,1) resonance frequency

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Figure 14

Predicted S-I field at (3,1) resonance frequency

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Figure 15

Measured S-I field at (3,1) resonance frequency

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Figure 16

Predicted S-I field at (2,3) resonance frequency

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Figure 17

Measured S-I field at (2,3) resonance frequency




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