An approximate procedure is developed for calculating the steady-state response of frictionally damped structures for which the normal load across the friction interface consists of a constant force and a force that varies linearly with the vibratory displacement. Such situations occur quite frequently in practice, as, for example; in the case of shrouded fan blades or in certain types of turbine-blade friction dampers. Depending on the magnitudes of the constant and the variable normal loads, the friction element will either stick, slip, or lift off at various intervals during a cycle of oscillation. The various possibilities are considered in the present study. Results from the approximate method are compared with “long-time” solutions obtained from a conventional transient analysis of the problem in order to assess the accuracy of the proposed procedure. As an application, the new method is then used to study the influence of the dynamic coupling on the optimization of the friction force in turbine blade dampers. Results show that the optimum friction force and the maximum amplitude of the response increase with dynamic coupling.

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