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TECHNICAL PAPERS

High-Frequency Low-Loss Ultrasonic Modes in Imbedded Bars

[+] Author and Article Information
B. N. Pavlakovic, M. J. S. Lowe, P. Cawley

Department of Mechanical Engineering, Imperial College, Exhibition Road, London SW7 2BX, U.K.

J. Appl. Mech 68(1), 67-75 (Aug 15, 2000) (9 pages) doi:10.1115/1.1347995 History: Received February 23, 2000; Revised August 15, 2000
Copyright © 2001 by ASME
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Figures

Grahic Jump Location
Phase velocity dispersion curves for (a) steel plate imbedded in grout; (b) steel bar imbedded in grout
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Phase velocity dispersion curves for F(1,1) mode of steel bar imbedded in “grout” of varying density (densities shown in kg/m3 )
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Phase velocity dispersion curves for a0 mode of steel plate imbedded in “grout” of varying density (densities shown in kg/m3 )
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Dispersion properties for a0 mode of steel plate imbedded in grout (a) attenuation; (b) phase velocity; (c) mode shape at minimum phase velocity (position A in (b))
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Dispersion curves of axisymmetric (L(0,n)) modes of steel bar imbedded in grout. (a) phase velocity; (b) attenuation; (c) energy velocity; (d) as (b) but zero steel attenuation.
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Mode shapes corresponding to points marked on Fig. 5. (a) point A; (b) point B; (c) point C. (—— axial displacement, – radial displacement, shaded—strain energy. Strain energy plotted in -ve direction to avoid confusion with axial displacement.)
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Phase velocity dispersion curves for steel bar imbedded in (a) grout; (b) epoxy; (c) glass; (d) cast iron. Imbedding medium has zero attenuation in these plots.
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Attenuation dispersion curves of first “crossing mode” of steel bar imbedded in cast iron, glass, and grout. (Grout case shown dotted for clarity.)
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Spectrum of response of signal transmitted through 2 m imbedded bar as excitation toneburst stepped between 3.0 and 8.0 MHz
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Maximum response as function of frequency. –imbedded bar results of Fig. 9; - - - - similar test on 50-mm-thick steel block. Note: The scales on the two plots are independently normalized.
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Predicted (- - - -) and measured (–) normalized attenuation curves for 8.1-mm steel bar imbedded in grout
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Time traces from tests on 8.1-mm steel bars imbedded in grout: pulse-echo tests on one bar with a 2-mm saw cut 450 mm into the grout and on another bar with a 4-mm saw cut 450 mm into the grout; through transmission test over 2 m length of undamaged imbedded bar. Excitation was 50 cycle, 3.75 MHz Hanning windowed toneburst.
Grahic Jump Location
Reflection of 5-cycle 5.2 MHz center frequency Gaussian windowed toneburst from 4-mm-deep notch in 8.1-mm-diameter imbedded bar. (a) Time domain signal; (b) wavelet transform of (a) showing amplitude as gray scale (black high) in time-frequency plane. Lines show predicted group delays obtained from energy velocity and overall propagation distance.

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