# A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints
## 3 Experimental Setup General Description and Design  
The layout and geometric features of the test rig are shown in Figure 4. Two identical rectangular beams (200 \(\times\) 40 \(\times\) 4 mm) are assembled by means of bolt (in this case, an M16 class 8.8 bolt is used). Four different contact interfaces result from the assembly: the contact interfaces between the two beams, the interfaces between the bolt head (or nut) and the upper (or the lower) surface of the beam A (or B), and the helical interface of the threads.  
In order to isolate the influence of the contact interface between the beams, another test rig consisting of one 200 \(\times\) 40 \(\times\) 8 mm monolithic beam is also manufactured for comparison purposes, as shown in Figure 4b. For both test rigs, the experimental frequency response functions (FRF) were measured and compared, in order to separate the nonlinear behavior associated with the small contact interfaces (i.e., the bolt head/beam A, the nut/beam B, and the threads), from that related to the large contact interface between the beams.  
Figure 4: Comparison of the two experimental setups: (**a**) two-beam joint, and (**b**) one monolithic beam.  
Figure 3: Deformation of the bolted flanges in vibration, (**a**) typical vibration modes of the bolted casing, (**b**) vibration shape of the flange, (**c**) deformed geometry of the single wave.  
For a preliminary assessment of the joint stress state under static load, a finite element (FE) nonlinear static analysis was carried out on the two-beam test rig in Ansys APDL. Each contact interface was modeled in a standard configuration by employing the contact elements CONTA174 and TARGE170 in the augmented Lagrangian formulation [29]. Pre-tension elements PRETS179 were also used to apply a reference tension preload of 10 kN at the bolt.  
The nonlinear static analysis results are shown in Figure 5, where the magnitude of the beams displacement along the bolt axis and the contact status at all the contact interfaces are represented by the colormaps. The results show that the region of the beams close to the bolt is tightly compressed, which leads to the sticking status of the contact interfaces (red area regions in Figure 5b). The outer diameter of the sticking area was estimated to be about twice the diameter of the bolt and it is fully included in the beams' width. A narrow sliding area (i.e., the orange region in Figure 5b) delimits the sticking region from the remaining part where separation occurs due to the receding contact [30]. The result is a continuing divergence of the wide nominal contact surfaces up to the edges, where the maximum clearance of 0.111 mm (along the beam length, points L and R in Figure 5a) was found.  
In order to investigate the vibration modes of the assembled bolted joint, a modal analysis was carried out using the linearized model, where the boundary conditions were set according to the contact status predicted as output of the nonlinear static analysis. As the method given in Ref. [31], the full compatibility of the displacements in all the directions is applied for the sticking area, the displacements compatibility in the normal direction is applied in the sliding area, and no boundary conditions are used for the separation area.  
The first bending mode shape of both test rig was identified and used for the identification of the experimental results (Figure 6). The mode shape shows two nodes at the bolt's sides and resembles a kinematics typical of the mode shapes of cyclic symmetric bolted flanges. The natural frequency obtained for the test rig mounting the monolithic beam was found much higher than that of the two-beam setup (854 Hz vs. 472 Hz).  
Figure 5: Nonlinear static analysis of the bolted joint, (a) displacements, and (b) contact status.  
Figure 6: Excited bending modes, (a) two-beam joint (472 Hz), (b) one monolithic beam (854 Hz).