Aeroelastic Flutter of a Rotating Disk in an Unbounded Compressible Inviscid Fluid

The aeroelastic flutter of an unbaffled flexible disk rotating in an unbounded fluid is investigated, by modeling the disk-fluid system as a rotating Kirchhoff plate coupled to irrotational flow of a compressible inviscid fluid. The fluid motions are governed by the wave equation of linear acoustics. Fluid-structure coupling is achieved between the disk and the fluid by means of the fluid loading on the disk and the velocity matching boundary conditions on the disk surface. A perturbed eigenvalue formulation is used to compute systematically the coupled system eigenvalues. A series solution is presented for the dual integral equations, arising from the mixed boundary value problem governing the fluid motions. It is found that two distinct aerodynamic effects occur — radiation damping into the surrounding fluid and added fluid inertia effect. Provided the disk has zero material damping, the radiation damping causes the flutter speed to coincide with the critical speed. This flutter instability is a degenerate bifurcation with eigenvalues crossing into the right half plane through the origin with zero speed. The added fluid inertia effect modifies the frequencies of the traveling waves but does not affect the critical speed.