# A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints
## 5 Dynamic Tests and Analysis
### Results for Different Bolt Tensional Loads  
Further tests were performed for the same set of excitation forces adopted in the previous tests, by varying the bolt tension. The typical results are shown in Figure 16 where the systems are excited with 1 N excitation amplitude and a range of variable bolt tension (1-9 kN). The experimental results show that for both structures, the response amplitude and natural frequency increase when the bolt tension increases from 1 to 9 kN. Numerical simulations suggest that for a bolt tension reduction from 7 to 1 kN, a contact pressure reduction takes place (Figure 17). This means that the smaller the bolt tension, the smaller the friction forces needed to trigger the slip status at the contact interface when the structure is dynamically excited. Thus, for the same excitation force, a structure with a smaller bolt tension features a higher amount of energy dissipated by friction. From Figure 16, it appears that the FRF of the two-beams bolted joint is more influenced by the bolt tension variation than those corresponding to the monolithic beam. In particular, the response amplitude of two beams in contact increases from 44.7 to 310.1 m/s\({}^{2}\)/N as the bolt tension increases from 1 to 9 kN, corresponding to a change of the 594%, while for the monolithic beam the increase of the peak response is 294.8% (from 166.9 to 658.9 m/s\({}^{2}\)/N as the bolt tension increases). Figure 16: Experimental FRFs influenced by the bolt tension, (**a**) two-beam joint, (**b**) one monolithic beam. Figure 17: Contact pressure of interfaces under, (**a**) small bolt tension (1 kN), (**b**) large bolt tension (7 kN). Similar to what has been observed on the effects of excitation forces, the FRFs peak amplitude is much more sensitive to the variation of the bolt tension rather than the peak frequency, which is caused by the greater variation of the damping induced at the sliding area. The influence of the bolt tension on the resonance frequency is larger than the excitation force. In fact, by keeping the excitation force fixed and equal to 1 N, an increase of the bolt tension from 1 to 9 kN generates an increase in the resonance frequency from 417 to 455.8 Hz for the two-beams joint system, corresponding to a 9.5% variation. The response versus the resonance frequency are shown in Figure 18, where the plotted curves refer to different bolt tensions and excitation amplitudes. The corresponding plots of the FRF amplitude versus the excitation forces are given in Figure 19.  
From Figure 18, it can be noted that the trends found for the response amplitudes with respect to the excitation force, (increasing from 0.1 to 2 N) are similar to each other for both test cases for the different bolt tension. The only exception is represented by the FRF obtained for the monolithic beam under 1 kN bolt tension. In particular, as the excitation force increases from 0.1 to 2.0 N, the FRF amplitude first decreases until the minimum corresponding to 0.5 N of excitation force is reached (Figure 19b), and then increases for all the remaining excitation levels. In this case, i.e., when the contact preload is small, sliding can occur at low excitation forces and be responsible for large energy dissipation. On the other hand, if the excitation force is so large that significant rela  
Figure 19: Characteristics of the FRF amplitudes versus the excitation force, (**a**) two-beam joint, (**b**) one monolithic beam. Figure 18: FRF peak point under various condition, (**a**) two-beam joint, (**b**) one monolithic beam. at the contact interfaces, the energy dissipation might result in low damping due to the inefficiency of the friction damping caused by the larger vibration amplitudes. Figure 20 shows the trends of the modal damping ratio \(\zeta\) identified using the rational fraction polynomials method versus the excitation forces at different bolt tension.