A receptance harmonic balance technique for the computation of the vibration of a whole aero-engine model with nonlinear bearings

Current frequency-domain techniques for the rapid computation of the steady-state periodic vibration of unbalanced rotordynamic systems with nonlinear bearings are not suitable for realistic engine structures like aero-engine assemblies. In this paper, a whole-engine receptance harmonic balance method (RHBM) is devised that, for the first time, allows the frequency domain analysis of such a structure. The method uses the receptance functions of the linear part of the structure under non-rotational conditions, obtained from a one-off eigenvalue analysis, to set up the equations for the rotating nonlinear assembly. The unknowns solved for are the Fourier coefficients of the relative displacements at the nonlinear bearings plus a few extra unknowns. These latter unknowns enable solution of the problem in the presence of statically indeterminate rotors that have just one linear point support or none at all. Simulation tests on a realistically sized representative twin-spool engine showed excellent correlation with time-marching results obtained from the recently developed impulsive receptance method (IRM). It is demonstrated that, when used in conjunction with a time-marching solver like the IRM, the RHBM is a very powerful tool that should greatly facilitate the hitherto highly restricted nonlinear dynamic analysis of realistic engine structures.