NDLI: General fractional derivative viscoelastic models applied to vibration elastography

Content Provider	IEEE Xplore Digital Library
Author	Liu, H. Oliphant, T.E. Taylor, L.
Copyright Year	2003
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Brigham Young Univ., Provo, UT, USA (Liu, H.; Oliphant, T.E.)
Abstract	In this work we derive general fractional-derivative-based viscoelastic models built from one, two, or three basic elements called viscoelastic springs. The basic viscoelastic spring used has a stress-strain relationship where stress is the fractional derivative of the strain. Fractional derivative models extend traditional Maxwell and Kelvin-Voigt viscoelastic models to allow for fractional powers of frequency in the Fourier domain. Combining these basic viscoelastic elements in series and in parallel results in increasingly complex models for the modulus as a function of frequency. We show how these models can be applied in the frequency domain to shear modulus data acquired using vibration elastography. Shear modulus data for curve fitting in the frequency domain were acquired using 10% and 15% bovine-gel mixtures (with added graphite particles) that were vibrated at 200 to 600 Hz in 100 Hz steps. The vibrations were detected using a 3.5 MHz ultrasound transducer. Shear modulus data for the same materials were also acquired using the dynamic mechanical analyzer (DMA 2980 from TA Instruments, Inc.) in a frequency range from 10Hz to 200Hz. Weighted least-squares fitting was used to determine the model parameters for two and three-element models applicable to viscoelastic solids. The results show that a two-element parallel combination of viscoelastic springs (the Kelvin-Voigt fractional derivative model) can somewhat explain the modulus data, though perhaps a three-element model generalizing the standard linear solid is more accurate over a wider frequency range.
Starting Page	933
Ending Page	936
File Size	125852
Page Count	4
File Format	PDF
ISBN	0780379225
DOI	10.1109/ULTSYM.2003.1293553
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-10-05
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Viscosity Elasticity Solid modeling Vibrations Springs Frequency domain analysis Stress Capacitive sensors Curve fitting Ultrasonic imaging
Content Type	Text
Resource Type	Article

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