A Method for the Assignment of Zeros Using Frequency Response Functions

In many engineering structures, undesirable harmonics can occur due to changes in operating conditions. The effects of these unwanted harmonics can be eliminated by assigning the zeros of point or cross Frequency Response Functions (FRFs) of the structure to the frequencies of the unwanted harmonics. In this study, a method is proposed for assigning the zeros of point or cross FRFs to particular frequencies.

The method is based on Sherman–Morrison (SM) formula known in matrix theory. The inverse structural modification problem was investigated by making spring modifications on a structure to assign zeros.

The required modifications are calculated by solving the set of equations containing nonlinear combinations of the spring coefficients.

There is no need for a physical or modal model of the structure because FRFs are used directly in the method. Therefore, it is quite practical in applications. The accuracy and efficiency of the presented method are illustrated by different numerical simulations and successful results are obtained.