Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources.
Previous studies by the second author published in this journal focused on low audible frequency (40-400 Hz) shear and surface wave motion in and on a viscoelastic material representative of biological tissue. Specific cases considered were that of surface wave motion on a halfspace caused by a finite rigid circular disk located on the surface and oscillating normal to it [Royston et al., J. Acoust. Soc. Am. 106, 3678-3686 (1999)] and compression, shear, and surface wave motion in a halfspace generated by a subsurface finite dipole [Royston et al., J. Acoust. Soc. Am. 113, 1109-1121 (2003)]. In both studies, a Voigt model of viscoelasticity was assumed in the theoretical treatment, which resulted in agreement between theoretical predictions and experimental measurements over a limited frequency range. In the present article, the linear viscoelastic assumption in these two prior works is revisited to consider a (still linear) fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time. It is shown that in both excitation source configurations, the fractional order Voigt model assumption improves the match of theory to experiment over a wider frequency range (in some cases up to the measured range of 700 Hz).
Meral
F Can
FC
Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
Royston
Thomas J
TJ
Magin
Richard L
RL
D000162:Acoustics / Q000295:instrumentation; D000465:Algorithms; D016014:Linear Models; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D011108:Polymers; D012828:Silicones; D013997:Time Factors; D055682:Viscoelastic Substances
D011108:Polymers; D012828:Silicones; D055682:Viscoelastic Substances