Correction to "Parametric Resonance in Immersed Elastic Boundaries"

TL;DR

This paper corrects errors in a previous study on the stability of a parametrically-forced elastic fiber in fluid, clarifying the conditions for parametric resonance and stability regions.

Contribution

It identifies and corrects two errors in the original derivation and computational analysis of the stability of immersed elastic boundaries.

Findings

Corrected the eigenvalue problem derivation

Fixed the computational code for stability contours

Clarified the stability regions for parametric resonance

Abstract

This note is a correction to a paper of Cortez, Peskin, Stockie & Varela [SIAM J. Appl. Math., 65(2):494-520, 2004], who studied the stability of a parametrically-forced, circular, elastic fiber immersed in an incompressible fluid in 2D, and showed the existence of parametric resonance. The results were represented as plots that separate parameter space into regions where the solution is either stable or unstable. We uncovered two errors in the paper: the first was in the derivation of the eigenvalue problem, and the second was in the code to used to calculate the stability contours.