24 M. Brøns et al. parameter in Eq. (3.1), why it covers any discrepancy between model and experiment. The frequencies of Bolt 1 and 3 can only fit to Eq. (3.1) if the effective length is unrealistically long. It suggests that the boundary stiffness does not entirely correspond to a clamped-clamped boundary, and the model is not sufficient in that case. 3.4 Conclusion Experiments has been performed with a real bolted structure to illustrate the challenges when working with real structures and multiple bolts. It was possible to measure and identify the first natural bending frequency of each mounted bolt and determine a damping ratio. However, the simple clamped-clamped beam model cannot in this case sufficiently explain the behaviour of the bolts. The experiments also showed a need to develop the experimental technique and signal processing to better separate the frequency peaks. Acknowledgments This work is financially supported by the Danish Council for Independent Research, grant DFF-6111-00385. References 1. Bickford, J.H.: Introduction to the Design and Behavior of Bolted Joints – Non-gasketed Joints, 4th edn. CRC Press, Boca Raton, FL (2007) 2. Joshi, S.G., Pathare, R.G.: Ultrasonic instrument bolt stress. Ultrasonics. 22(6), 270–274 (1984) 3. Nassar, S.A., Veeram, A.B.: Ultrasonic control of fastener tightening using varying wave speed. J Press Vessel Technol. 128(3), 427 (2006) 4. Sah, S.M., Thomsen, J.J., Brøns, M., Fidlin, A., Tcherniak, D.: Estimating bolt tightness using transverse natural frequencies. J Sound Vib. 431, 137–149 (2018). https://doi.org/10.1016/j.jsv.2018.05.040 5. Thomsen, J.J.: Vibrations and Stability: Advanced Theory, Analysis, and Tools. Springer, New York (2003)
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