On Stability Analysis of a Flexible Cylinder in an Array of Rigid Cylinders

The concept of an unsteady control volume is used to predict the onset of instability for a simple array of cylinders. The array consists of a flexible cylinder placed amidst rigid cylinders. The fluid is assumed to be incompressible with a “slip” boundary condition used on the solid/liquid interface. The equations derived for the model from first principles are solved in the complex plane. The results are compared to experimental data. The paper is concluded with a discussion of the advantages and disadvantages of the model and an assessment of the accuracy of the predictions.