Numerical Methods for Computing the Frequency Response

In vehicle dynamics the frequency range of interest is between 0.1 Hz and 20 Hz. These frequencies are important for discussing the systems basic behavior, the ride comfort and safety criteria. Within this range G iuj) has to be evaluated for a dense grid of frequency values. Thus, several hundred matrix inversions might be necessary in order to get an accurate picture of this function. Therefore it pays off to discuss different possibilities to simplify this task as much as possible. 

The problem can easily be transformed into the equivalent real one 

The effort for this foregoing, with A being squared, is 

The minimal computational effort for computing G iuj) = C iujl — A) B can be achieved by first transforming A to a block diagonal form by means of similarity transformations. For this we have to assume that A is diagonalizable 

The system (2.5.9a) can be transformed into block diagonal form with 4x4 blocks. This reduces significantly the computational effort for solving this system. The total effort is 

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