# A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints
## 1 Introduction  
Bolted joints are widely used for the assembly of mechanical components to provide continuity of the structure and transfer internal actions (i.e., forces and moments) from one member to another. Typical applications of bolted joints can be found in aircraft turbo-engines where bolted flanges are largely employed to connect turbine or casing stages (Figure 1). The dynamical response of structures assembled by bolts is significantly influenced by the damping due to friction at all the contact interfaces, i.e., those between the two parts held together, the screw threads, and the interfaces between the bolt head/nut and the parts (Figure 1c). In this regard, it has been proved that most of the structural damping comes from the bolted joints instead from the material, especially in structures made of metal [1]. Reported damping ratios for monolithic metallic structures are small, typically between 0.0001 and 0.001, while the damping ratio of built-up structures with joints is in the order of 0.01, with friction providing up to the 90% of the total structural damping [2]. The dynamic behavior of built-up structures assembled by bolted joints, as well as the structural damping resulting from the nonlinear behavior of the joints, has drawn the attention of researchers since the early stage of the 20 th century [3]. A series of experimental investigations on either bolted flanges or bolted beams were reported by [PERSON] [4], [PERSON] [5], [PERSON] [6], and [PERSON] [7] et al. A usual comparison between the one-piece structure and the equivalent built-up system proved that the main source of damping is the joint instead of the material [8]. For instance, in bolted flanges, it has been observed that damping is mainly induced by the partial contact area surrounding the bolt, which is limited with respect to a wider potential contact area, due to the occurrence of receding contact. In this region, the contactpressure distribution in the vicinity of the bolt hole rapidly decreases from the center towards the outer region (Figure 2a) [9], causing the micro-slip [10]. An in-plane relative motion at the contact interface will be responsible for the micro-slip in the regions where the normal pressure is not large (Figure 2b) [11]. Under the action of a cyclic excitation, the micro-slip involves energy dissipation and a reduction of vibration amplitudes. Nevertheless, contact interfaces between the bolt head/nut and flange, as well as the screw threads, might also provide a non-negligible amount of friction damping if certain vibration modes are excited at resonance. In this frame, the experimental tests play a crucial role in most of the published studies, and various test rigs and experimental measurement techniques have been developed in recent past years in several laboratories worldwide [12]. In most of these tests, the relationship between the tangential force and the in-plane displacement is investigated, in order to identify the hysteresis behavior and obtain the damping and stiffness parameters of the bolted joint [13]. Quasi-static tests in bolted flanges on a universal testing machine were carried out by [PERSON] [14] and [PERSON] [15]. However, due to the simple experimental setup, no conclusions can be inferred from a dynamical point of view. For this reason, in the Gaul resonator designed at the University of Stuttgart for lap joints [16], the dynamic excitation was applied by means of an electromagnetic shaker. A similar dynamic test rig called dumbbell oscillator, was developed at the Sandia National Laboratories [12]. The test  
Figure 1: Illustration of bolted joints, (**a**) bolted flanges, (**b**) overlap joints, (**c**) the contact interfaces. Figure 2: Illustration of a bolted joint, (**a**) Qualitative representation of the pressure distribution [9], (**b**) Sliding in the contact patch [11]. rig, which was also used by [PERSON] and [PERSON] et al.