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Research Papers

Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition

[+] Author and Article Information
Boyang Ding

Zhejiang University of Technology,
Hangzhou 310014, China
e-mail: dingboyang@zjut.edu.cn

Alexander H.-D. Cheng

University of Mississippi,
Oxford, MS 38677-1848
e-mail: acheng@olemiss.edu

Zhanglong Chen

Zhejiang University of Technology,
Hangzhou 310014, China
e-mail: chenzhanglong@yeah.net

1Corresponding author.

Manuscript received December 5, 2012; final manuscript received February 3, 2013; accepted manuscript posted February 19, 2013; published online August 21, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech 80(6), 061021 (Aug 21, 2013) (12 pages) Paper No: JAM-12-1546; doi: 10.1115/1.4023692 History: Received December 05, 2012; Revised February 03, 2013; Accepted February 19, 2013

Fundamental solutions of poroelastodynamics in the frequency domain have been derived by Cheng et al. (1991, “Integral Equation for Dynamic Poroelasticity in Frequency Domain With BEM Solution,” J. Eng. Mech., 117(5), pp. 1136–1157) for the point force and fluid source singularities in 2D and 3D, using an analogy between poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on the decomposition of a Dirac δ function into a rotational and a dilatational part. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken. These isolated wave fields may be useful in applications where it is desirable to separate the shear and compressional wave effects. These wave fields are evaluated and plotted.

FIGURES IN THIS ARTICLE
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Copyright © 2013 by ASME
Topics: Fluids , Waves , Displacement
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Figures

Grahic Jump Location
Fig. 1

Real (solid line) and imaginary (dashed line) part of x-component displacement of shear wave, u˜11s, due to an instantaneous point force in the x-direction, at f=10 Hz. (a) Along the x-axis, and (b) along the y-axis.

Grahic Jump Location
Fig. 2

Three dimensional plot of shear wave y-component displacement u˜21s on the x-y plane, due to an instantaneous point force in the x-direction, at f=10 Hz. (a) Real part, and (b) imaginary part.

Grahic Jump Location
Fig. 3

Contour plot of shear wave y-component displacement u˜21s on the x-y plane, due to an instantaneous point force in the x-direction, at f = 10 Hz. (a) Real part, and (b) imaginary part.

Grahic Jump Location
Fig. 4

Real (solid line) and imaginary (dashed line) part of x-component displacement of the first compressional wave, u˜11p1, due to an instantaneous point force in the x-direction, at f = 10 Hz. (a) Along the x-axis, and (b) along the y-axis.

Grahic Jump Location
Fig. 5

Three dimensional plot of first compressional wave y-component displacement u˜21p1 on the x-y plane, due to an instantaneous point force in the x-direction, at f = 10 Hz. (a) Real part, and (b) imaginary part.

Grahic Jump Location
Fig. 6

Real (solid line) and imaginary (dashed line) part of x-component displacement of the second compressional wave, u˜21p2, due to an instantaneous point force in the x-direction, at f = 10 Hz. (a) Along the x-axis, and (b) along the y-axis.

Grahic Jump Location
Fig. 7

Real (solid line) and imaginary (dashed line) part of x-component displacement of combined wave solution, u˜11Force, due to an instantaneous point force in the x-direction, at f = 10 Hz. (a) Along the x-axis, and (b) along the y-axis.

Grahic Jump Location
Fig. 8

Real (solid line) and imaginary (dashed line) part of x-component displacement, due to an instantaneous fluid source, at f = 10 Hz. (a) The first compressional wave, and (b) the second compressional wave.

Grahic Jump Location
Fig. 9

Real (solid line) and imaginary (dashed line) part of pressure, due to an instantaneous fluid source, at f = 10 Hz. (a) The first compressional wave, and (b) the second compressional wave.

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