## 3 Influence of Key Parameters on the Response
### Contact Model: Influence of Contact Parameters  
Another important factor influencing the forced response prediction is the choice of contact model parameters. As stated before, a contact model is adopted to approximate the contact between strip and blade platforms. The contact model consists of springs (normal, \(k_{n}\), and tangential stiffnesses, \(k_{tx}\), \(k_{ty}\)) acting between the contact nodes of the strip and the blade. The \"nominal\" values come from an extensive experimental campaign performed on rigid dampers experiencing contact pressures in the range of those experienced by the present strip damper [39] and are reported in Table 1. However, the different contact conditions, kinematics and compliance of the strip damper may result in changes of the contact model calibration parameters. An ad-hoc investigation has been performed to investigate the influence of the contact parameters: resonance frequency predictions are plotted as function of a stiffness multiplying factor (\(SMF\)).  
As shown in Figure 13 different simulations were run considering the neck-bending mode shape at two different (extreme) exciting Engine Order (EO) (The engine order (EO) is an integer indicating the number of times each blade is excited during each complete rotation of the disk. A different EO excites a different nodal diameter, inducing a different vibration phase among two consecutive blades). In detail:  
* EO = 0 means that the blades vibrate with the same phase, that is In-Phase (IP).
* EO = 22 (that is the number of the blades 44 divided by two) means that the blades vibrate with opposite phase, that is Out-of-Phase (OOP).  
Both Figures 13a and b show that, by increasing the contact stiffnesses values, the natural frequency of the system increases. This is not surprising since, if the springs are stiffer, the nodes are less able to vibrate.  
Moreover, the effect of normal and tangential stiffnesses depends on the phase between the consecutive blades connected by the strip. For the IP mode (EO = 0), the normal stiffness has higher influence. This can be explained considering that, during the IP mode, the blade-strip relative displacement is mainly along the vertical direction (i.e., \(k_{n}\) normal stiffness direction), as sketched in Figure 14. Conversely, for the OOP mode (EO = 22) \(k_{n}\) has no influence and only the tangential  
Figure 13: Neck-bending mode shape. (**a**) Influence of contact stiffnesses for In-Phase (IP) (1320 Hz) motion. (**b**) Influence of contact stiffnesses for Out-of-Phase (OOP) (1366 Hz) motion.  
stiffness \(k_{t}\) affects the dynamic behavior. The reason is that, for the OOP mode, the strip slips mainly along the tangential direction, as sketched in Figure 14.  
The authors are aware that the determination of the true contact stiffness values to be used in the numerical calculation is still an open question. A dedicated experimental campaign, similar to the one performed for rigid dampers [42] is underway. Still gaining a full awareness of the influence each parameter has on the numerical prediction is a necessary step in the creation of a meaningful experimental campaign.