## 3 Influence of Key Parameters on the Response  
The ultimate goal and output of the numerical tool is the forced response prediction of the blade-strip system. In detail, designers are particularly interested in the amplitude and frequency position of the resonance point (maximum of the Frequency Response Function (FRF) curve). Out of these two parameters, the frequency position is particularly relevant. In fact, the resonance frequency is used by designers to determine how likely that resonance is to be excited by the engine order excitation applied to the disk, and, for this reason, it is the main focus of this investigation. An example of forced response curves is shown in Figure 4a. The blue dotted curve, here termed \"Free\", refers to the linear case of the blades without strip dampers to act as additional constraints and is typically estimated faultlessly using commercial FE codes. The presence of the strip damper requires instead an ad-hoc numerical tool, described in Section 2 and represented in Figure 3.  
The red solid curve, here termed \"Stick\", is another linear limit case where the strip damper is stuck to the corresponding blade platforms and the relative motion is allowed only by the elastic deformation at the contact through the contact stiffnesses (it is nevertheless a coupled mode). The full stick condition is not only a \"limit case\" but is encountered for low excitation levels (high \(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|\) ratio). In the full stick condition, the presence of the strip dampers reduces (in this case in a negligible manner) the amplitude of the response and shifts the peak to a higher frequency. Being able to predict effectively the frequency shift is paramount to a safe and robust design. As the level of excitation increases (and the \(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|\) ratio decreases) the relative displacement at the contact will exceed the friction limit and contacts will start to slip. As a result, part of the global contact stiffness is lost and the resonant frequency shifts to lower values (i.e., it moves back towards the \"Free\" condition). Furthermore, friction-induced dissipation limits the FRF amplitude (the peak will appear as \"less sharp\", as shown in the \(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|=15\) case in Figure 4a). For extremely high excitation levels (e.g., \(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|=4\)) the strip will lose contact with the blade platforms during vibration and the resonance frequency and amplitude will draw even closer to the \"Free\" condition. The resonance frequency is depicted in Figure 4b as a function of the excitation level. As observed above, the frequency is maximum in \"Stick condition\" (\(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|>50\)) and gradually moves towards the \"Free frequency\" for decreasing \(|\mathbf{F_{c}}|/|\mathbf{F_{ex}}|\) ratios. It is here shown that the way the contact is modelled has a large impact on the frequency shift prediction. Figure 4b shows how different contact parameters used as input to the contact model will lead to different FRF peaks. The largest difference can be found, unsurprisingly, in the linear/weakly nonlinear regime, where the complete contact stiffness is at play. Conversely, in the nonlinear regime, the influence of different modelling choices (i.e., in this case different contact parameter values) is less severe. The present investigation will therefore focus on the linear/weakly nonlinear regime. Figure 3: Scheme of the solving procedure and corresponding key engineering/modelling decisions. It should be noted that the value of contact parameters is not the only modelling choice that affects the resonance frequency prediction. As shown in Figure 3, the designer has to face a series of modelling decisions when it comes to representing the strip damper and the blade-strip contact interface. The full list of the key parameters to be chosen at the different design/modelling steps is found below. 1. The mesh size in the FE model of the contact areas. 2.