Structure-preserving frequency analysis and linearization of spatially discrete rotating systems

Noise-Vibration-Harshness is an engineering discipline, aiming to achieve an optimized vibro-acoustic experience for complex assemblies, such as passenger cars. A great portion of the tools at hand rely on a linear formulation of the input-output behavior. However, it is crucial that each subsystem is expressed in an autonomous formulation such that it fits to the complete system setup and becomes amenable for direct computations in the frequency domain.

I illustrate how such a change of observer can be realized when the chosen modeling approach is spatially discrete. In this work, I define a notion of stationarity that incorporates symmetries of the governing equations and their solutions. I proceed to embed these discrete symmetry requirements into a continuous framework, making use of continuous 1-parameter groups of linear operators. Eventually, it is possible to construct a coordinate transformation that turns the system into an autonomous one, keeping the physical structures of the systems intact. The theory behind this change of observer, however, is quite a general one, not relying on detailed knowledge of the system in question or the computation of eigenmodes.