On e cient and adaptive modelling of friction damping in bladed disks

High cycle fatigue failure of turbine and compressor blades due to resonance in the operating frequency range is one of themain problems in the design of gas turbine engines. To suppress excessive vibrations in the blades and prevent high cycle fatigue, dry friction dampers are used by the enginemanufacturers. However, due to the nonlinear nature of friction contact, analysis of such systems becomes complicated. This work focuses on the efficientmodelling of friction contact and adaptive control of friction damping in bladed disks. To efficiently simulate the friction contact problem, a 3D time-discrete contact model is reformulated and an analytical expression for the Jacobian matrix is derived in parallel to the contact forces. The analytical expression drastically reduces the computation time of the Jacobian matrix with respect to the classical finite difference method, with many points at the contact interface. Therefore, it also significantly reduces the overall computation time for the solution of the equations of motion, since the formulation of the Jacobian matrix is the most time consuming step in solving the large set of nonlinear algebraic equations when a finite difference approach is employed. The developed numerical solver is successfully applied on bladed disks with shroud contact and the advantage of full-3D contact model compared to a quasi-3D contactmodel having uncoupled tangentialmotion is presented. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different harmonic indices (nodal diameters) of the bladed disk are systematically presented. The developed numerical solver is also applied on bladed disks with strip damper and multiple friction contacts. The equations ofmotion are formulated in the frequency domain using themultiharmonic balancemethod to accurately capture the nonlinear contact forces and displacements. Moreover, the equations ofmotion of the full bladed diskmodel are reduced to a single sector model by exploiting the concept of the cyclic symmetry boundary condition for a periodic structure. The main parameters that influence the effectiveness of friction damping in bladed disks are engine excitation order, interface parameters (normal and tangential contact stiffness and friction coefficient), relative motion at the friction interface and the normal contact load at the interface. Due to variation in the interface parameter values during operation and also these parameters are oftenhard to predict at the design level, the obtained friction damping in practice may differ significantly from the optimum value. Therefore, to control the normal load adaptively that will lead to an optimum damping in the system despite these variations, use of magnetostrictive actuator is proposed in this work. The magnetostrictive material that develops an internal strain under the influence of an external magnetic field is used to increase and decrease the