Gas and steam turbine applications are exposed to high vibration amplitudes. Friction damping elements are commonly used to prevent blades from fatigue failure. Most of the work done so far in this field is dealing with steady state vibration occurring due to harmonic excitation. Regarding the growing importance of renewable energy, the number of run-ups and rundowns in power plants is increasing continuously. Furthermore, also the speed of jet engines is changed regularly during operation. To give an analytical approach on how to calculate and create most effective friction damping during instationary excitation, this paper discusses the computation of transient nonlinear vibration. Following the description of a single-degree-of-freedom system comprising a friction contact, it is shown how to assemble the equation of motion using piecewise linear equations. An analytical ansatz is illustrated to solve the ODEs of the system. In the next step, two simple multi-body-systems are created that are coupled by a friction contact. To validate the analytical computation of the vibration response of the system, a numeric time integration of the system is done. The calculations are compared, and it is shown that the analytical ansatz is valid to compute the vibration of the system. Using the solution of the equation of motion of the multi-body-system, it is shown how the optimal friction damping of the system can be determined while varying important parameters like e.g. the normal force of the friction contact and the tangential stiffness of the contact model.

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