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

VL - 46

SP - 331

EP - 340

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 3-4

ER -