## 4 Application
### Scenario  
The application for our approach arises the vehicle chassis development in the digital design phase. We use the first conceptual FE model of a knuckle. This component connects the wheel and the brakes via the suspension links to the car body or the subframe. All structure-born noise from the road and the brake passes the knuckle. We modify the transfer path between wheel hub and suspension links by changing the component's design in order to modify the chassis noise transfer. An illustration of the knuckle is presented in Figure 7.  
Figure 7: Illustration of the used knuckle. The kinematic hard point \(P\) for the connection to the track rod is located in the center of the gray area on the left side. The large gray area on the right represents the connection to the wheel hub. In the scenario for this paper, we fix the knuckle at the wheel hub via stiff springs against fixed ground. The stiffness and frequency range is selected in a way; it creates rigid body modes of the knuckle on the springs and elastic modes of the component itself. This represents a simplified test case as it could occur in a full axle. We calculate the FRFs between all the suspension link hard points and the wheel hub force. By changing the location of one of the kinematic hard points to the suspension links, we investigate the influences on the FRFs. We investigate a displacement of \(\pm 10\,\mathrm{mm}\) of the hard point \(P\) between knuckle and track rod in three directions. We create 100 designs using space filling latin hypercube by varying the \(x_{1}\), \(x_{2}\) and \(x_{3}\) coordinates. We call the original coordinate \(x_{0}\) and the received design coordinate \(x_{DoE}\). We restrict the displacement in the cubical design space to a sphere with \(10\,\mathrm{mm}\) radius \(r\) and the center point \(P\) with the coordinate \(x_{0}\). Designs with the Euclidean distance  
\[d=|x_{DoE}-x_{0}|>r \tag{13}\]  
violate the sphere. These points are shifted towards \(P\) to the sphere's surface in order to condense the information on the border. This method follows one of the three suggestions by [20] (p. 221). We calculate the new coordinate on the surface  
\[x_{border}=x_{0}+\frac{r}{d}\left(x_{DoE}-x_{0}\right)\quad\text{for}\quad d >r\quad. \tag{14}\]  
For the study in this paper, we investigate the FRF between the hard point \(P\) for the track rod connection in the direction along the track rod (\(x_{2}\)), marked by the blue arrow on the left in Figure 7 and wheel hub in vertical direction (\(x_{3}\)), marked by the blue arrow on the right. This FRF represents the transfer path of vertical excitation from the road to vibrations induced into the track rod. The FRF is given in Figure 8.  
We chose the peak at \(777\,\mathrm{Hz}\) with an amplitude of \(6.68\,\mathrm{NN}^{-1}\) for our investigation. We can reduce the amplitude by two means. We can either reduce the peak's amplitude or change the peak's frequency. The latter is equivalent to changing an eigenmode's frequency [4; 17]. In a first step, we compare the FRF range of both morphing approaches for the 100 designs that we generated. In Figure 9 we show the FRF introduced in Figure 8 with an additional Skyline overlay. The gray Skyline indicates the lowest and highest amplitude for all 100 designs. Figure 8: FRF between hard point track rod in \(x_{2}\)-direction and wheel hub in \(x_{3}\)-direction. \(777\,\mathrm{Hz}\) in blue. Moving the hard point by an absolute value of up to \(10\,\mathrm{mm}\) around the original attachment point clearly offers a wide variety of changing the FRF, especially in the higher frequency range in which the elastic modes dominate. Both morphing approaches result in similar amplitude bands. Nevertheless, especially at \(777\,\mathrm{Hz}\), the maximum and minimum amplitudes of the Skyline vary by \(8.5\,\mathrm{\char 37}\) and \(17.6\,\mathrm{\char 37}\) respectively, with the smaller possible changes resulting from Direct Morphing. We discuss the reasons for that after discussing the optimization results.