Stability and Forced Response of Beam-Like Structures Having Negative Viscous Damping and Displacement-Dependent Dry Friction Damping

Abstract

Abstract The flexural vibration of a beam-like structure damped with a displacement-dependent Coulomb friction force is examined. Due to the geometry of the dry friction damping element, the friction force grows linearly with the beam’s transverse displacement. Recent studies have shown that the damping of systems with displacement-dependent dry friction forces resembles linear structural damping. Taking advantage of this fact, the energy loss per cycle can be made to grow like the square of the vibratory displacement amplitude rather than linearly with amplitude as in the case of frictionally damped systems with constant normal forces. Furthermore, dry friction is well suited to hostile environments such as the high temperatures and high rotation speeds associated with gas turbines. These observations suggest that displacement-dependent dry friction may be an effective means of flutter suppression in turbine and fan blade applications. Destabilizing aerodynamic forces are represented in this study as negative viscous damping. This simple aerodynamic model is often used to capture the basic features of flutter in aeroelastic systems. Both single and multiple-mode analyses are conducted. Results show that energy losses from the displacement-dependent dry friction damper are large enough to overcome the destabilizing negative viscous damping under certain conditions. This result further suggests that it may be possible to design the geometry and location of frictional interfaces in turbine blade systems so that damping may be enhanced and flutter better controlled.