Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

Gorb, Yuliya; Walton, Jay R.

Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

Type

Article

Authors

Gorb, Yuliya
Walton, Jay R.

KAUST Grant Number

KUS-C1-016-04

Date

2010-11

Abstract

We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.

Citation

Gorb Y, Walton JR (2010) Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress. International Journal of Engineering Science 48: 1289–1312. Available: http://dx.doi.org/10.1016/j.ijengsci.2010.09.002.

Acknowledgements

This publication is based on work supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The work of Y. Gorb was partially supported by NSF grants DMS-0811180 and DMS-1016531.