TY - JOUR
T1 - Homogenizing the time-harmonic acoustics of bone
T2 - The monophasic case
AU - Fang, Ming
AU - Gilbert, Robert P.
AU - Panchenko, Alexander
AU - Vasilic, Ana
N1 - Funding Information:
This research was supported in part by NSF grant INT 0438765 and by an Alexander v. Humboldt Senior Scientist Award at the Ruhr University Bochum. Ming Fang is partially supported by NSF grant HRD-0207971 and Norfolk State University Faculty Summer Research Grant.
PY - 2007/8
Y1 - 2007/8
N2 - For the interrogation of cancellous bone using ultrasound, we undertake a derivation of the time-harmonic, acoustic equations, idealizing the bone as a periodic arrangement of a Kelvin-Voigt viscoelastic porous matrix containing a viscous fluid. Since we are interested in acoustics, rather than filtration, we assume that the fluid is slightly compressible. Moreover, we study the monophasic case. A priori estimates are obtained for the time-harmonic equations. By letting the characteristic size of the inhomogeneities tend to zero and passing to the limit in the sense of the two-scale convergence, the effective equations for the monophasic vibrations are obtained, for which we prove existence and uniqueness.
AB - For the interrogation of cancellous bone using ultrasound, we undertake a derivation of the time-harmonic, acoustic equations, idealizing the bone as a periodic arrangement of a Kelvin-Voigt viscoelastic porous matrix containing a viscous fluid. Since we are interested in acoustics, rather than filtration, we assume that the fluid is slightly compressible. Moreover, we study the monophasic case. A priori estimates are obtained for the time-harmonic equations. By letting the characteristic size of the inhomogeneities tend to zero and passing to the limit in the sense of the two-scale convergence, the effective equations for the monophasic vibrations are obtained, for which we prove existence and uniqueness.
KW - Time-harmonic waves
KW - Two scale convergence
KW - Viscoelasticity of Kelvin-Voigt
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U2 - 10.1016/j.mcm.2006.10.005
DO - 10.1016/j.mcm.2006.10.005
M3 - Article
AN - SCOPUS:34247877825
SN - 0895-7177
VL - 46
SP - 331
EP - 340
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 3-4
ER -