# A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints
## 7 Conclusions  
The dynamical characteristics of the bolted flanges during the out of plane vibration were experimentally investigated in this paper. A new, simple test rig was designed to highlight the nonlinear effect of a single bolted joint by controlling the bolt preload and the excitation amplitude. The frequency response functions of the bolted structures, as well as the damping, are studied, and the effects of the excitation force amplitudes and the bolt tension are analyzed. From the application of the test rig to different bolted joint systems, the following conclusions can be drawn within the scope of this study:  
1. By comparing the dynamical characteristics of the two-beams bolted joint with that of the monolithic beam, it can be proved frictional damping induced at the interfaces between two flanges is the main source of the structural damping. Roughly speaking, the contribution of the interfaces between flanges to the modal damping ratio is not less than 2/3 of the total.
2. However, the nonlinear characteristic of the bolted monolithic beam clearly show how the dynamical characteristics of the bolted structures are also affected by the other contact areas of the joint (i.e., the interface between the head/nut and flange, or threads in contact). Thus, the influence of other contact areas of joints also needs to be considered in the study of the bolted structures.
3. As the excitation force increases, both the natural frequency and the response amplitude decrease nonlinearly, which can be explained by the nonlinear stiffness and damping caused by the contact interfaces. Micro-slip is more likely to occur at the contact interfaces as the excitation force increase, leading to more energy dissipation (i.e., damping) and lower tangential stiffness. Similar results are obtained by varying the bolt preload.
4. According to the experimental results of bolted beams with different contact areas at the head/nut, the amplitude of the structure with smaller contact interfaces is higher than that with larger interfaces under the same loading condition. The testing results further proved that the contact interfaces between the bolt head (or nut) and the flange has an important influence on the dynamic response of the structure.  
Figure 24: FRFs of bolted joints with small interfaces, influence of (**a**) excitation force, (**b**) bolt tension.  
**Author Contributions:** Conceptualization, C.M.F. and J.H.; methodology, C.M.F. and Y.W.; software, G.B.; validation, Y.W.; formal analysis, Y.M.; investigation, Y.W.; resources, C.M.F.; data curation, Y.W.; writing--original draft preparation, Y.W.; writing--review and editing, C.M.F. and Y.M.; visualization, Y.W. and G.B.; supervision, C.M.F. and J.H.; funding acquisition, C.M.F. and J.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the AerMec Laboratory of the Politecnico di Torino and the National Natural Science Foundation of China (Nos. 52075018).  
**Informed Consent Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank the National Natural Science Foundation of China (Nos. 52075018), and the China Scholarships Council (No. 201906020037) for their support in this research.  
The authors declare no conflict of interest.