## 1 Introduction  
Turbine blades do not benefit significantly from material hysteresis and aerodynamic damping [1; 2; 3]. Therefore, in order to prevent high vibration amplitude, the best option is to add external sources of damping, e.g., in the form of dry friction devices [1; 4]. Dry friction can be incorporated into the blade design, in the form of shrouds [5; 6; 7; 8], interlocked contact surfaces [9], lacing wires or zigzag pins. Alternatively, external devices such as solid dampers (available in several designs, namely cylindrical, curved flat, wedge damper, etc. [10; 11; 12; 13; 14; 15; 16] or thin-strip dampers [17] can be added to minimize the resonant blade response. These external dry friction dampers are extensively used in turbine designs because they are easy to manufacture, install and substitute, relatively inexpensive and can withstand high temperatures. Among external dry friction dampers, the strip (or seal) dampers are thin flexible metallic strips which are positioned under the blade platforms of turbine bladed disks and their primary function is for cooling-air sealing purpose. They are pushed against the blade platforms by the centrifugal force. When relative motion takes place between strip and blade platforms, the friction forces dissipate vibrational energy and consequently the dynamic response of the system is damped. In this way the strips act both as friction dampers and as an additional constraint affecting the blade natural frequencies. The design of the strips, not only for sealing, but also for damping purpose, represents a topic of recent interest for the turbine designers, as very few studies can be found in literature [4; 17]. In the past 15 years, the so-called solid underplatform dampers (UPDs) have been extensively investigated [18; 19; 20; 21; 22; 23; 24]. Most of the proposed calculation methodologies for bulk UPDs use simplifying assumptions, such as neglecting the damper inertia or flexibility [11; 19; 25]. However, these assumptions, perfectly adequate for solid UPDs, cannot be applied to model strip dampers, as they are highly flexible and consequently their flexible vibrational modes need to be taken into account in the modelling process through FE modelling [17]. In the present work the strip damper is in fact modelled using Finite Elements. Furthermore, the most advanced state-of-the-art calculation methods are here applied to predict the dynamic of two blades and a strip damper between them. In detail, the nonlinear forced response is calculated with high computational efficiency in the frequency domain using the multi-harmonic balance method (MHBM) [26; 27; 28], a reduction method is adopted to decrease the size of the blades [29] and the nonlinear equations are solved by an iterative solver using the analytical computation of the Jacobian matrix [28; 30; 31]. Lastly a novel technique presented in [32] ensures that the MHBM (an approximate method) offers results with an accuracy above a user-defined threshold. The key features of the numerical tool used in this paper are summarized in Section 2. Even if preliminary calculations of the blade forced responses show the expected trend with excitation force and centrifugal force, it is shown that the natural frequency and vibration amplitude strongly depend on the choice of some key parameters. Purpose of this paper is to address the choice of these key parameters and explore the consequences of each choice on the predictions offered by the numerical simulation tool. The following key topics are addressed. 1. The strip damper is modelled using finite elements given its high flexibility. Does the mesh discretization, especially around the contact area, significantly affect results? 2. A subset of nodes is selected on the strip damper contact area and contact elements are applied to take into account the presence of friction. A uniform distribution of contact elements seems to be the most logical choice, but does the selected pattern (and number of contact elements) affect the position of the resonant frequencies? 3.