Investigation of Transducer Mass Loading Effect in Frequency Response Function (FRF)

The accuracy and the reliability of various analyses using the measured FRFs depend strongly on the quality of measured data. It is well known that the quality of measured frequency response functions (FRFs) is adversely affected by many factors, most significant sources being noise and systematic errors like mass loading effects of transducers. A transducer mounted on a vibrating system changes the dynamics of the structure due to the addition of extra mass and introduces errors into measured FRFs. One problem with this is the production of unrealistic results, which cause the measured resonant frequencies to be less than the correct values. These errors also lead to incorrect prediction of modal parameters. In many situations, the mass loading effect is ignored in the analytical and experimental Modelling process, based on a usual assumption that the transducer mass is negligible compared to that of the structure under test. However, when light-weighted structures are investigated, this effect can be significant and it may be necessary to eliminate this undesirable side effect before the measured data are used for further analyses.

     The mass loading effects of accelerometer and force transducer can be eliminated from measured FRFs (including point FRF and transfer FRF) in shaker modal testing. Considering different sensors for response measurements, two common collocations in shaker modal testing are investigated: (1) shaker + Laser Doppler  vibrometer case, in which only force transducer mass loading effects need to be removed, and (2) shaker + accelerometer case, in which both accelerometer and force transducer mass should be eliminated.

     The Sherman-Morrison identity for the elimination of mass loading effects of accelerometers from measured FRF. The formulation presented can be applied for both fixed transducer (hammer testing) and moving transducer (shaker testing) case. In moving transducer case, a dummy mass is utilized. Also, the transducer mass loading effect on the transfer FRFs can be removed by considering a set of measurements using two accelerometers with different masses. Sometimes, the effect of the extra masses on a measured FRF can be cancelled by cancellation technique for transducers at the driving points.

     The resonance frequencies of the plate measured with an accelerometer are lower than those of measured without accelerometer. However, after the elimination of the effect of the mass difference between the two accelerometers, both the natural frequencies and the FRFs as a whole are in quite good agreement with the target values.