Frictional instabilities in orthotropic hollow cylinders

This study discusses the implications of obstacle curvature, material orthotropy and friction to the occurrence of flutter and divergence instabilities of elastic media. The analytic solution for the divergence instability problem of a hollow cylinder when its principal directions of orthotropy make constant angles with the circumferential and radial directions is closely approximated by finite element solutions of a complementarity eigenproblem in which the coefficient of friction appears as an eigenvalue, quadratically due to the obstacle curvature. Mechanical systems with a finite number of degrees of freedom illustrate some aspects of the onset of instability. In particular, the presented study shows that, under certain conditions, the increase of the obstacle convexity may favour stability.