Dynamics of a flexible cylinder in subsonic axial flow

This paper examines the dynamics of a flexible cylinder with pinned ends immersed in axial subsonic flow, either bounded or unconfined. The problem proves to be surprisingly resistant to exact solution, as compared to the incompressible flow case, because of difficulties in determining precisely the inviscid aerodynamic forces. This paper presents a number of distinct formulations of these forces, involving different approximations: 1) a slender-body approximation; 2) an approximate three-dimensional formulation where, in the determination of the aerodynamic forces, the axial mode shape is prescribed in advance; and 3) an "exact" integral formulation of the generalized aerodynamic forces. In each case, Galerkin-type solutions yield the system eigenfrequencies which describe the dynamical behavior of the system. It is found that for sufficiently high flow velocities, divergence and flutter are possible. The different methods yield similar, but not quantitatively identical results. Interestingly, dependence of the dynamical characteristics on Mach number is shown to be weak for slender cylinders; for nonslender ones, it is stronger. Finally, a brief discussion of wave propagation in an unconstrained cylinder indicates the existence of a cutoff flow velocity for backward propagating waves, followed by wave amplification at higher flow, which is closely related to loss of stability in the constrained system.