An Acoustic Model for Wave Propagation in a Weak Layer

[+] Author and Article Information
Michael El-Raheb

 ATK Mission Research, 23052 Alcade Drive, Laguna Hills, CA 92653

J. Appl. Mech 72(5), 744-751 (Feb 07, 2005) (8 pages) doi:10.1115/1.1988367 History: Received December 21, 2004; Revised February 07, 2005

An acoustic model is developed for transient wave propagation in a weak layer excited by prescribed pressure or prescribed acceleration at the boundary. The validity of the acoustic model is investigated for the two excitations. A comparison of transient response from the acoustic model and a 3D axisymmetric elastic model reveals that for prescribed acceleration the acoustic model fails to capture important features of the elastic model even as Poisson ratio ν approaches 12. However for prescribed pressure, the two models agree since shear stress is reduced. For prescribed acceleration adopting the modal approach, the mixed boundary-value problem on the excited boundary is converted to a pure traction problem utilizing the influence method. To validate the elaborate modal approach a finite difference model is also developed.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Acoustic histories from prescribed pressure: —, r=0; ---, r=0.5rp; – – –, r=0.9rp. (a1), (b1) modal; (a2), (b2) finite difference.

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Figure 2

Frequency spectra of elastic and acoustic models. (a) Elastic model; (b) acoustic model.

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Figure 3

Prescribed motion at footprint. (a) Acceleration; (b) velocity; (c) displacement.

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Figure 4

Comparison of elastic and acoustic histories for prescribed acceleration: —, r=0; ---, r=0.5rp; – – –, r=0.9rp. Elastic model: (a1) w(r,0), (b1) σzz(r,0), (c1) σzz(r,h); acoustic model: (a2) w(r,0), (b2) σzz(r,0), (c2) σzz(r,h).

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Figure 5

Acoustic histories from prescribed pressure: —, r=0; ---, r=0.5rp; – – –, r=0.9rp. (a) w(r,0;t); (b) p(r,0;t); (c) p(r,h;t).

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Figure 6

Acoustic pressure and displacement profiles at z=0 and t=4μs. (a1), (b1) Prescribed acceleration; (a2), (b2) prescribed pressure.

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Figure 7

Variation of pmx with acceleration parameters U0 and Δt13. (a1), (b1) z=0; (a2), (b2) z=h.

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Figure 8

Effect of Poisson ratio ν on (a) deformation snapshots at t=8μs: (a1) ν=0.470, (a2) ν=0.495; (b) variation of peak stress with ν

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Figure 9

Comparison of analytical and finite volume elastic models: —, r=0.02rp; ---, r=0.5rp; – – –, r=0.96rp. (a1), (b1) w, σzz analytical.

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Figure 10

Comparison of w histories from elastic and acoustic models with prescribed pressure: —, r=0; ---, r=0.5rp; – – –, r=0.9rp

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Figure 11

Comparison of σzz histories from elastic and acoustic models with prescribed pressure: —, r=0; ---, r=0.5rp; – – –, r=0.9rp



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