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Research Papers

On Power Flow Suppression in Straight Elastic Pipes by Use of Equally Spaced Eccentric Inertial Attachments

[+] Author and Article Information
Sergey Sorokin

 Department of Mechanical and Manufacturing Engineering, Aalborg University Pontoppidanstraede 101, Aalborg East, DK 9220, Denmarksvs@m-tech.aau.dk

Ole Holst-Jensen

 Minus10dB Stokrosevej 29, DK 8330 Beder, Denmarkole.holst@minus10db.dk

J. Vib. Acoust 134(4), 041003 (May 31, 2012) (9 pages) doi:10.1115/1.4005652 History: Received December 15, 2010; Revised June 07, 2011; Published May 29, 2012; Online May 31, 2012

The paper addresses the power flow suppression in an elastic beam of the tubular cross section (a pipe) at relatively low excitation frequencies by deploying a small number of equally spaced inertial attachments. The methodology of boundary integral equations is used to obtain an exact solution of the problem in vibrations of this structure. The power flow analysis in a pipe with and without equally spaced eccentric inertial attachments is performed and the effect of suppression of the energy transmission is demonstrated theoretically. These results are put in the context of predictions from the classical Floquet theory for an infinitely long periodic structure. Parametric studies are performed to explore sensitivities of this effect to variations in the number of attachments. The theoretically predicted eigenfrequencies and insertion loss are compared with the dedicated experimental data.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Translational and rotational displacements, force, and moment resultants in a pipe (in a beam with tubular cross section)

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Figure 2

The inertial attachment

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Figure 3

Bloch parameters for a pipe with spans of 700 mm: the first stop band. Dotted curve: coupled flexural-longitudinal wave propagation; triangle-marked curve: uncoupled flexural wave propagation; circle-marked curve: uncoupled axial wave propagation. (a) Propagation constants (ImKB=0, ReKB>0). (b) |λ| in the coupled problem. (c) |λ| in the uncoupled problems.

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Figure 4

Bloch parameters for a pipe with spans of 700 mm: the second stop band. Dotted curve: coupled flexural-longitudinal wave propagation; triangle-marked curve: uncoupled flexural wave propagation; circle-marked curve: uncoupled axial wave propagation. (a) Propagation constants (ImKB=0, ReKB>0). (b) |λ| in the coupled problem. (c) |λ| in the uncoupled problems.

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Figure 5

The effect of number of equally spaced masses (700 mm spans) in the semi-infinite beam (triangle-mark curves—three inclusions, circle-marked curves—five inclusions, continuous curves—seven inclusions). (a) Flexural excitation and (b) longitudinal excitation.

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Figure 6

The incremental IL effect of two equally spaced masses (700 mm spans) in the idealized semi-infinite setup (circle-marked curve—adding to the pipe with three inclusions, dotted curve—adding to the pipe with five inclusions)

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Figure 7

The effect of number of masses in the pipe of the finite length (triangle-marked curve—three inclusions, circle-marked curve—five inclusions, thin continuous curve—seven inclusions)

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Figure 8

Experimental setup: (a) Pipe structure with periodic inertial attachments and (b) the “sandwich structure”

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Figure 9

Comparison of theoretical predictions with experimental data (thin continuous curve—experiment, circle-marked curve—theory)

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