Vibrations in finitely deformed residual stressed circular cylindrical tubes

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

A residually stressed thick-walled tube is subject to a combination of internal or external pressure and axial stretch to maintain its circular cylindrical geometry. A small incremental motion is then superimposed on the finitely deformed configuration. We summarize the basic elements of the theory of hyperelasticity with initial stress, together with the corresponding incremental forms. Equations are derived and used to evaluate the dependence of the axial load, of the vibration frequency and of the circumferential stress, on the inner and outer curved boundaries, on the residual stress and on various geometric quantities. The theory is applied to a simple neo-Hookean model with two material parameters and a parameter to scale the magnitude of the residual stress. The static response to small incremental deformations is obtained as a special case when the vibration frequency vanishes.

Details

Original languageEnglish
Pages (from-to)174-195
Number of pages22
JournalMathematics and Mechanics of Solids
Volume28
Issue number1
Early online date13 Jun 2022
Publication statusPublished - Jan 2023
Peer-reviewedYes

External IDs

Scopus 85132114366
Mendeley f1294c61-0507-3c45-97f0-f3c90cf59437