Relative scaling of mode shapes using transmissibility functions

• From operational modal analysis only unscaled mode shapes/eigenvectors are found.
• Transmissibility functions are used to determine the scaling factor of each mode.
• The method requires a general knowledge of the input force locations.
• The method can also used when not all force input locations are known.
• From the found scaling factors the transfer function can be rebuilt.

Operational modal analysis (OMA) is the collective term for different techniques that estimate the modal parameters of a linear structure using only the structural responses to unknown excitations. Therefore, OMA is the preferred approach when operational forces are hard to measure, when operational conditions are hard to replicate in a controlled environment or when an experimental modal analysis (EMA) is too time-consuming. However, OMA does not allow us to determine the relative contribution of each mode, i.e. the mode shapes found with OMA are unscaled.This paper introduces a novel approach to estimate the relative contributions of all modes within a given bandwidth and to reconstruct frequency response functions (FRF) that are proportional to the true FRFs of the system. This novel technique requires only response data and a general knowledge of the input locations of the dominant forces acting on the system. It is shown that even when only a limited number of input locations are known the proposed method can still be used by considering multiple loading conditions. Finally, since the technique is based on transmissibility functions, there are no necessary assumptions considering the spectral content of the excitations.Several numerical examples illustrate the claimed properties and are used to quantify the influence of measurement and ambient noise.