Generation of the whole FRF matrix from measurements on one column

摘要

It is customary in modal testing to measure one column or one row of the FRF matrix in order to develop the mathematical model that represents the dynamic behaviour of a structure. The unmeasured FRFs can, in principle, be synthesised from the measured FRFs using the modal properties. However, generating the unmeasured FRFs from the measured ones along a single row or column is only theoretically possible when the frequency range covered extends from zero to infinity. In practice, it is necessary to limit the frequency range of measurement for obvious reasons. The remaining part, due to the out of range modes - the residual - is not available and, as a result, estimating the unmeasured FRFs from the measured ones is not accurate unless values for the relevant residual terms can be estimated. In the past, some efforts have been made to relate the residual effects of out-of-range modes between measured and unmeasured FRFs, but without much success. The purpose of the present article is to describe a method for evaluating the whole FRF matrix using one accelerometer and one dummy mass. The method is theoretically based on the direct substructuring technique: Structural Modification Using experimental frequency Response Functions (SMURF). The method is exact but in practical situations may be vulnerable to noise. Noise has been considered in the FRFs and the way to prevent the errors is presented.