A method to solve the efficiency-accuracy trade-off of multi-harmonic balance calculation of structures with friction contacts

The steady-state nonlinear forced response of systems with frictional damping can be computed in the frequency domain through the Harmonic Balance Method (HBM). A critical point is the selection of the number of harmonic terms used to represent the solution. In linear systems, this number is easily determined by the harmonic content of the forcing function (e.g. mono-harmonic). However, if nonlinearities are present, higher order harmonics may need to be included to ensure a proper representation of friction forces and displacements, with a detrimental effect on the computational time.The paper presents a novel method to solve the efficiency-accuracy trade-off of harmonic selection for nonlinear systems. This method warns the user whenever the number of retained harmonic terms is inadequate. As a result, it enables the user to run the simulation with a low number of retained harmonics, e.g. designers are typically interested in the first harmonic of the solution. The calculation is repeated with a larger harmonic support only when strictly necessary to keep the error below a user-defined threshold.The method is first compared to existing adaptive HBM techniques, highlighting its novel contributions. It is then carefully validated against high-order multi-harmonic calculations and against direct time integration. Its performance in terms of accuracy vs. computational time is highlighted. The method is then implemented in a state-of-the-art numerical tool for the design of underplatform dampers for turbine blades. Finally, its outcome is compared with experimental results.