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TECHNICAL PAPERS

# Experimental and Numerical Investigation of Structural Damage Detection Using Changes in Natural Frequencies

[+] Author and Article Information
G. Y. Xu, B. H. Emory

Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250

W. D. Zhu1

Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250

1

Corresponding author.

J. Vib. Acoust 129(6), 686-700 (Jan 19, 2007) (15 pages) doi:10.1115/1.2731409 History: Received June 05, 2006; Revised January 19, 2007

## Abstract

A robust iterative algorithm is used to identify the locations and extent of damage in beams using only the changes in their first several natural frequencies. The algorithm, which combines a first-order, multiple-parameter perturbation method and the generalized inverse method, is tested extensively through experimental and numerical means on cantilever beams with different damage scenarios. If the damage is located at a position within $0–35%$ or $50–95%$ of the length of the beam from the cantilevered end, while the resulting system equations are severely underdetermined, the minimum norm solution from the generalized inverse method can lead to a solution that closely represents the desired solution at the end of iterations when the stiffness parameters of the undamaged structure are used as the initial stiffness parameters. If the damage is located at a position within $35–50%$ of the length of the beam from the cantilevered end, the resulting solution by using the stiffness parameters of the undamaged structure as the initial stiffness parameters deviates significantly from the desired solution. In this case, a new method is developed to enrich the measurement information by modifying the structure in a controlled manner and using the first several measured natural frequencies of the modified structure. A new method using singular value decomposition is also developed to handle the ill-conditioned system equations that occur in the experimental investigation by using the measured natural frequencies of the modified structure.

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## Figures

Figure 13

Cantilever aluminum beam specimen with evenly distributed damage between 14.8cm and 20cm from the cantilevered end and a tip mass of 5% of that of the cantilever beam

Figure 14

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 14.8cm to 20cm from the clamped end by setting all σi=1 and using the first two (—), three (−∘−), four (−•−), and five (−▴−) measured natural frequencies of the beam without and with the tip mass. A 90-element FE model is used.

Figure 3

Iterative algorithm for identifying the stiffness parameters of the damaged structure using only the changes in its measured natural frequencies

Figure 4

Experimental results for the estimated bending stiffnesses of the undamaged beam by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies, and a 90-element FE model

Figure 5

Experimental results for the estimated bending stiffnesses of the beam with a cut by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies, and a 45-element FE model

Figure 6

Experimental results for the estimated bending stiffnesses of the beam with two cuts by using the first five measured natural frequencies, and 45-element (−∘−), 90-element (−•−), and 135-element (−▴−) FE models

Figure 7

Cantilever aluminum beam specimen with evenly distributed damage between 9.6cm and 15cm from the cantilevered end

Figure 8

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 9.6cm and 15cm from the cantilevered end by using: (a) the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies; and (b) the first six (−∘−), seven (−•−), and eight (−▴−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 9

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 24.6cm and 30cm from the cantilevered end by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies, and a 90-element FE model

Figure 10

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 14.8cm to 20cm from the cantilevered end by setting σi=1(i=1,2,…,m) and using the first three (−∘−), four (−•−), five (−▴−), and six (−×−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 11

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 14.8cm to 20cm from the cantilevered end by setting σi=0.4 for 0.35≤i∕m≤0.50 and σi=1 elsewhere, and using the first three (−∘−), four (−•−), five (−▴−), and six (−×−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 12

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 14.8cm to 20cm from the cantilevered end by setting all σi=1 and using the first four (−•−), five (——), and six (×) measured natural frequencies. Every ten neighboring elements are grouped together in a 90-element FE model.

Figure 1

Cantilever aluminum beam specimen with two cuts: (a) scale drawing and (b) experimental setup

Figure 2

Comparison of the first four ((a)-(d)), analytical (——) and numerical (−×−, ΔGi=0.1; •, ΔGi=0.0001) eigenvalue sensitivities of an undamaged, 45-element, cantilevered beam along its length

Figure 17

Simulation results for the estimated bending stiffnesses of the beam with two cuts by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 18

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 10cm to 15cm from the cantilevered end by using the first three (−∘−), four (−•−), five (−▴−), and eight (−×−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 19

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 25cm to 30cm from the cantilevered end by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies with ε=0.001, and the first three (−×−) measured natural frequencies with ε=0.0001. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 20

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 15cm to 20cm from the cantilevered end by setting all σi=1 and using the first three (−∘−), four (−•−), five (−▴−), and six (−×−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 21

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 15cm to 20cm from the cantilevered end by setting σi=0.4 for 0.35≤i∕m≤0.50 and σi=1 elsewhere, and using the first three (−∘−), four (−•−), five (−▴−), and six (−×−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 22

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 15cm to 20cm from the cantilevered end by setting all σi=1 and using the first four (−•−), five (——), and six (×) measured natural frequencies: (a)ε=0.001 and (b)ε=0.0001. Every ten neighboring elements are grouped together in a 90-element FE model.

Figure 23

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage between 15cm to 20cm from the cantilevered end by setting all σi=1 and using the first two (——), three (−∘−), four (−•−), and five (−▴−) measured natural frequencies of the beam without and with the tip mass. A 90-element FE model is used.

Figure 24

Simulation results for the estimated bending stiffnesses of the beam with evenly distributed damage from 20cm to 25cm from the cantilevered end by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 15

Experimental results for the estimated bending stiffnesses of the beam with evenly distributed damage between 20cm and 25.2cm from the cantilevered end by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

Figure 16

Simulation results for the estimated bending stiffnesses of the beam with a cut by using the first three (−∘−), four (−•−), and five (−▴−) measured natural frequencies. Neighboring elements are grouped in pairs in a 90-element FE model.

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