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Journal of Vibration and Acoustics | Volume 135 | Issue 6 | Technical Brief
Technical Briefs

Modulation Spectroscopy of Acoustic Waves in Solids Containing Contact-Type Cracks

[+] Author and Article Information
T. C. Tszeng

Department of Mechanical Engineering,
Santa Clara University,
Santa Clara, CA 95053

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 8, 2011; final manuscript received May 9, 2013; published online August 6, 2013. Assoc. Editor: Liang-Wu Cai.

J. Vib. Acoust 135(6), 064504 (Aug 06, 2013) (6 pages) Paper No: VIB-12-1028; doi: 10.1115/1.4025017 History: Received November 08, 2011; Revised May 09, 2013
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Citing Articles

This study examined the characteristics of sidebands in modulation spectroscopy on a high-frequency wave interacting with a defect that imposes a simple switching type disruption caused by a low-frequency, high-amplitude vibration. A simple close form of sideband amplitude is obtained by convolution of a high-frequency probing wave with harmonics of a pulse wave. This study also proposes an experimental procedure based on sideband phases for determining the crack parameters.
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Figures

Grahic Jump Location
Fig. 1

(a) Example of spectrum of a modulated probing wave as calculated by FFT. fa = 1000 Hz, fv = 20 Hz, σc/Av = 0.4, and R between 0.1 and 0.9. (b) Examples of changes of measured spectra with an increasing number of fatigue cycles on aluminum alloy 6082 [12].

+(a) Example of spectrum of a modulated probing wave as calculated by FFT. fa = 1000 Hz, fv = 20 Hz, σc/Av = 0.4, and R between 0.1 and 0.9. (b) Examples of changes of measured spectra with an increasing number of fatigue cycles on aluminum alloy 6082 [12].
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(a) Example of spectrum of a modulated probing wave as calculated by FFT. fa = 1000 Hz, fv = 20 Hz, σc/Av = 0.4, and R between 0.1 and 0.9. (b) Examples of changes of measured spectra with an increasing number of fatigue cycles on aluminum alloy 6082 [12].
Grahic Jump Location
Fig. 2

Schematic of interaction between a crack and signal transmission. The probing signal is attenuated by a factor R during the period in which the pumping signal exceeds the crack opening threshold strength σC. Diagrams shows the pulse wave resulting from crack switching behavior between close and open. R is the transmission factor. It is shown that the pulse width τ/T=α/π+1/2 (see text).

+Schematic of interaction between a crack and signal transmission. The probing signal is attenuated by a factor R during the period in which the pumping signal exceeds the crack opening threshold strength σC. Diagrams shows the pulse wave resulting from crack switching behavior between close and open. R is the transmission factor. It is shown that the pulse width τ/T=α/π+1/2 (see text).
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic of interaction between a crack and signal transmission. The probing signal is attenuated by a factor R during the period in which the pumping signal exceeds the crack opening threshold strength σC. Diagrams shows the pulse wave resulting from crack switching behavior between close and open. R is the transmission factor. It is shown that the pulse width τ/T=α/π+1/2 (see text).
Grahic Jump Location
Fig. 3

Calculated strength (in decibels) of the first three sidebands (S1, S2, and S3) plotted against parameter R for two different values of σc/Av (and therefore β). Aa = Av/100. (a) σc/Av = 0.75 and (b) σc/Av = 0.

+Calculated strength (in decibels) of the first three sidebands (S1, S2, and S3) plotted against parameter R for two different values of σc/Av (and therefore β). Aa = Av/100. (a) σc/Av = 0.75 and (b) σc/Av = 0.
View Large  |  Save Figure  |  Download Slide (.ppt)
Calculated strength (in decibels) of the first three sidebands (S1, S2, and S3) plotted against parameter R for two different values of σc/Av (and therefore β). Aa = Av/100. (a) σc/Av = 0.75 and (b) σc/Av = 0.
Grahic Jump Location
Fig. 4

Calculated strength of the first three sidebands (in decibels) plotted against σc/Av for R = 0.2 and 0.8. Aa = Av/100.

+Calculated strength of the first three sidebands (in decibels) plotted against σc/Av for R = 0.2 and 0.8. Aa = Av/100.
View Large  |  Save Figure  |  Download Slide (.ppt)
Calculated strength of the first three sidebands (in decibels) plotted against σc/Av for R = 0.2 and 0.8. Aa = Av/100.
Grahic Jump Location
Fig. 5

Calculated relative strength of the first three sidebands plotted against σc/Av for (a) R = 0.2 and (b) 0.8. Aa = Av/100.

+Calculated relative strength of the first three sidebands plotted against σc/Av for (a) R = 0.2 and (b) 0.8. Aa = Av/100.
View Large  |  Save Figure  |  Download Slide (.ppt)
Calculated relative strength of the first three sidebands plotted against σc/Av for (a) R = 0.2 and (b) 0.8. Aa = Av/100.
Grahic Jump Location
Fig. 6

FFT calculated strength of the first two sidebands (in decibels) plotted against v for R = 0.2 and 0.8. Aa = Av/2.

+FFT calculated strength of the first two sidebands (in decibels) plotted against v for R = 0.2 and 0.8. Aa = Av/2.
View Large  |  Save Figure  |  Download Slide (.ppt)
FFT calculated strength of the first two sidebands (in decibels) plotted against v for R = 0.2 and 0.8. Aa = Av/2.

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