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A Study on the Relationship of Embedded Sensitivity With Measuring Grid and Mode Shapes

[+] Author and Article Information
Marcos Satoshi Kawamoto

Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, Trabalhador São-Carlense 400, 13566-590 São Carlos, São Paolo, Brazil

Rodrigo Nicoletti

Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, Trabalhador São-Carlense 400, 13566-590 São Carlos, São Paolo, Brazilrnicolet@sc.usp.br

J. Vib. Acoust 133(2), 024503 (Mar 03, 2011) (5 pages) doi:10.1115/1.4002127 History: Received August 19, 2009; Revised June 01, 2010; Published March 03, 2011; Online March 03, 2011

Embedded sensitivity analysis has proven to be a useful tool in finding optimum positions of structure reinforcements. However, it was not clear how sensitivities obtained from the embedded sensitivity method were related to the normal mode, or operational mode, associated to the frequency of interest. In this work, this relationship is studied based on a finite element of a slender sheet metal piece, with preponderant bending modes. It is shown that higher sensitivities always occur at nodes or antinodes of the vibrating system.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Finite element model of the sheet metal

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Figure 2

Embedded sensitivities to stiffness among grid points (first bending mode): (a) dH53,53/dk (grid 1), (b) dH83,83/dk (grid 2), and (c) dH83,83/dk (grid 3)

Grahic Jump Location
Figure 3

Embedded sensitivities to stiffness among grid points (second bending mode): (a) dH53,53/dk (grid 1), (b) dH33,33/dk (grid 2), and (c) dH43,43/dk (grid 3)

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Figure 4

Embedded sensitivities to stiffness among grid points (third bending mode): (a) dH53,53/dk (grid 1), (b) dH83,83/dk (grid 2), and (c) dH83,83/dk (grid 3)

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Figure 5

Embedded sensitivities to stiffness among grid points (fourth bending mode): (a) dH53,53/dk (grid 1), (b) dH63,63/dk (grid 2), and (c) dH63,63/dk (grid 3)

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Figure 6

Embedded sensitivities to stiffness among grid points (fifth bending mode): (a) dH53,53/dk (grid 1), (b) dH83,83/dk (grid 2), and (c) dH83,83/dk (grid 3)

Grahic Jump Location
Figure 7

Embedded sensitivities to torsion stiffness among grid points (first bending mode): (a) dH53,53/dτ (grid 1), (b) dH83,83/dτ (grid 2), and (c) dH83,83/dτ (grid 3)

Grahic Jump Location
Figure 8

Embedded sensitivities to torsion stiffness among grid points (second bending mode): (a) dH53,53/dτ (grid 1), (b) dH33,33/dτ (grid 2), and (c) dH43,43/dτ (grid 3)

Grahic Jump Location
Figure 9

Embedded sensitivities to torsion stiffness among grid points (third bending mode): (a) dH53,53/dτ (grid 1), (b) dH83,83/dτ (grid 2), and (c) dH83,83/dτ (grid 3)

Grahic Jump Location
Figure 10

Embedded sensitivities to torsion stiffness among grid points (fourth bending mode): (a) dH53,53/dτ (grid 1), (b) dH63,63/dτ (grid 2), and (c) dH63,63/dτ (grid 3)

Grahic Jump Location
Figure 11

Embedded sensitivities to torsion stiffness among grid points (fifth bending mode): (a) dH53,53/dτ (grid 1), (b) dH83,83/dτ (grid 2), and (c) dH83,83/dτ (grid 3)

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