The aerodynamic interference between the blades of a bladed disk can lead to self-excited vibrations known as flutter. Flutter vibrations can reach considerable levels and are thus of special concern in the design of turbomachines. The vibrations can be saturated in so-called limit cycles by the nonlinear dissipative effects related to dry friction in mechanical joints. For a given mode family of a tuned bladed disk, the flutter stability depends on the interblade phase angle, and often multiple traveling wave forms are unstable. In spite of this, previous investigations indicated that in the steady state, friction-damped flutter vibrations of tuned bladed disks are dominated by a single traveling wave component. In contrast, we demonstrate that, in fact, multiple traveling wave components may interact in the steady state. To this end, a phenomenological model is studied, which possesses one lumped mass per sector, elastic Coulomb friction inter-sector coupling, and two unstable traveling waves forms. Depending on the location of the complex eigenvalues of the linearized system, the steady-state vibrations are shown to be dominated by either of the two unstable wave forms or exhibit considerable contributions of both. Both periodic and quasi-periodic attractor forms are computed using Fourier methods and validated with direct time integration. Moreover, the basins of attraction of the different stable limit states are analyzed in detail. Remarkably, even if a stable, periodic vibration in a certain traveling wave is attained, a sufficiently strong instantaneous perturbation of the same form can give rise to a transient ending in a limit cycle with a different traveling wave character.
Validation of a Modal Work Approach for Forced Response Analysis of Bladed Disks
