Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials

Journal of the Acoustical Society of America

Volumn 115, Issue 2, 2004, Pages 893-900

  Wu, Junru ^a   Layman, Christopher ^a   Liu, Jun ^b  

^a University of Vermont   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC DISPERSION; CONTINUUM MECHANICS; LOW DENSITY POLYETHYLENES; SHEAR WAVES; TISSUE; ULTRASONIC PROPAGATION; WAVE EQUATIONS;

DOUBLET MECHANICS; LONGITUDINAL WAVES; SOFT TISSUES;

BIOMATERIALS;

BIOMATERIAL; NANOMATERIAL; POLYETHYLENE; UNCLASSIFIED DRUG;

ACOUSTICS;

ARTICLE; DENSITY; DISPERSION; DOUBLET MECHANICS; FREQUENCY MODULATION; KRAMERS KRONIG RELATION; LONGITUDINAL STUDY; MATERIALS TESTING; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; MATHEMATICS; PRIORITY JOURNAL; SHEAR FLOW; SOFT TISSUE; SOUND; SOUND TRANSMISSION; ULTRASOUND; VAN HOVE SINGULARITIES MODEL; WAVE EQUATION; WAVEFORM;

COMPUTER SIMULATION; ECHOENCEPHALOGRAPHY; ELASTICITY; HUMANS; MECHANICS; MODELS, THEORETICAL; NANOTECHNOLOGY; PHANTOMS, IMAGING; POLYETHYLENE; ULTRASONOGRAPHY;

EID: 1042276663     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1642620     Document Type: Article

References (16)

1. Auld, B. A. (1990). Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, Malabar, Fl), pp. 251-253.
2. Bamber, J. C. (1986). "Speed of sound," in Physical Principles of Medical Ultrasonics, edited by C. R. Hill (Ellis Horwood Limited, New York), pp. 200-224.
3. Ferrari, M., Granik, V. T., and Imam, A. (1997). "Introduction to doublet mechanics," in Advances in Doublet Mechanics, edited by M. Ferrari, V. T. Granik, and A. Imam (Springer-Verlag, Berlin), pp. 1-26.
4. Ferrari, M. (2000). "Nanomechanics, and biomedical nanomechanics: Eshelby's inclusion and inhomogeneity problems at the discrete/continuum interface," Biomed. Microdevices 2, 273-281.
5. Ferrari, M. (2003). Private communication.
6. Granik, V. T. (1997). "Comparison with other theories," in Advances in Doublet Mechanics, edited by M. Ferrari, V. T. Granik, and A. Imam (Springer-Verlag, Berlin), pp. 51-82.
7. He, P. (1999). "Experimental verification of models for determining dispersion from attenuation," IEEE Trans. UFFC 46, 706-714.
8. He, P. (2000). "Measurement of acoustic dispersion using both transmitted and reflected pulses," J. Acoust. Soc. Am. 107, 801-806.
9. Kittel, C. (1971). Introduction to Solid State Physics (Wiley, New York), p. 214.
10. Kremkau, F. W., Barnes, R. W., and McGraw, C. P. (1981). "Ultrasonic attenuation and propagation speed in normal human brain," J. Acoust. Soc. Am. 70, 29-38.
11. Liu, J., and Ferrari, M. (2002). "Mechanical spectral signatures of malignant disease? A small-sample, comparative study of continuum vs. nanobiomechanical data analyses," Disease Markers 18, 175-183.
12. O'Donnell, M., Jaynes, E. T., and Miller, J. G. (1981). "Kramers-Kronig relationship between ultrasonic attenuation and velocity," J. Acoust. Soc. Am. 69, 696-701.
13. Szabo, T. L. (1994). "Time domain wave equations for lossy media obeying a frequency power law," J. Acoust. Soc. Am. 96, 491-500.
14. Szabo, T. L., and Wu, J. (2000). "A model for longitudinal and shear wave propagation in viscoelastic media," J. Acoust. Soc. Am. 107, 2437-2446.
15. Tobolsky, A. T. (1960). Properties and Structure of Polymers (Wiley, New York).
16. Wu, J. (1996). "Determination of velocity and attenuation of shear waves using ultrasonic spectroscopy," J. Acoust. Soc. Am. 99, 2871-2875.