PSI - Issue 71

Faisal Hussain et al. / Procedia Structural Integrity 71 (2025) 248–255

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to introduce additional vibrations or alter the behavior of the system as time progresses. The graph depicting the relationship between frequency and acceleration indicates the presence of resonates and non-linearity, providing insights on the vibrational behavior of the cantilever beam. The coefficient indicated above represents the cubic stiffness element in the mathematical framework used for analysis. The exact value of cubic stiffness nonlinearity and estimated value shows a high degree of closeness with a percentage of error within the proximity range of 5%. This implies that the mathematical model offers an exceptional estimation of the real system's behavior and demonstrates a significant level of accuracy. The findings from the experiments conclusively illustrate a correlation between the frequency and the movement of the secure end of the beam. The resonance movement will be altered by variations in stiffness. The cubic stiffness non-linearity at different amplitudes and frequencies will affect the system's response. 5. Conclusion The primary objective of this investigation is to create a method for accurately determining the nonlinear structure parameters. The sub-structure synthesis concept is used to get the frequency equations. The developed equation was used for an inverse analysis, in which data that were acquired theoretically were used to estimate a non-linear parameter. Through curve fitting non-linear region amplitude response was determined, which revealed cubic stiffness non-linearity in the angular stiffness parameter. The method is validated by employing numerical case studies that imitate experimental measurements using mathematically produced data. The results demonstrate satisfactory agreement between the assumed and estimated values. Evidence shows that a process is resistant to measurement errors. The collection of data indicates that the suggested method can effectively be applied to real constructions. The current model used for estimating joint parameters can be improved. This method has been developed specifically for the stiffness estimation of joint parameters. The development of nonlinear system modeling, identifying parameter processes, and the implementation of dynamic nonlinear simulation software can be done simultaneously in further research work. Also, by developing several optimization techniques, more focus can be given to identifying the non-linear joint parameters that can precisely determine the structural joints behavior under dynamic conditions. References Doranga, S., Wu, C., 2021. Study of nonlinear effects in a bolted joint using the base excitation as an input. Journal of Vibro engineering 23, 1109 – 1128. Hussain, F., Ingole, S., 2022. A Review on Frequency Domain Analysis Approach for Parametric Identification of Nonlinear Joints. Recent Advances in Machines and Mechanisms: Select Proceedings of the iNaCoMM 2021, 79–96. Hussain, F., Ingole, S., 2024. Non - linear modeling and parameter identification of a bolted joint using substructure synthesis theory. Engineering Research Express 6, 1 - 17. Hussain Faisal, Ingole Sanjay, 2024. Enhancing Joint Parameter Identification with Sub Structure Synthesis Theory: A Non - linear Perspective. Romanian Journal of Acoustics and Vibration 21, 3–11. Ingole, S.B., Chatterjee, A., 2010. A method for joint stiffness identification. In: AIP Conference Proceedings. 338–343. Ingole, Sanjay B., Rajurkar, S.W., 2022. Nonlinear Joint Stiffness Parameter Identification. In: Lecture Notes in Mechanical Engineering,379 392. Jalali, H., Bonab, B.T., Ahmadian, H., 2011. Identification of Weakly Nonlinear Systems Using Describing Function Inversion. Exp Mech 51, 739–747. Jamia, N., Jalali, H., Taghipour, J., Friswell, M.I., Haddad Khodaparast, H., 2021. An equivalent model of a nonlinear bolted flange joint. Mech Syst Signal Process 153,1 - 18. Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C., 2006. Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process,505 - 592. Kim, W. - J., Lee, B. - Y., Park, Y. - S., n.d. 2004, Non - linear joint parameter identification using the frequency response function of the linear substructure,947 - 955. Lacayo, R.M., Allen, M.S., 2019. Updating structural models containing nonlinear Iwan joints using quasi - static modal analysis. Mech Syst Signal Process 118, 133–157. Noël, J.P., Kerschen, G., 2017. Nonlinear system identification in structural dynamics: 10 more years of progress. Mech Syst Signal Process 83, 2–35. Volkova, V., 2013. Development of methods for nonparametric identification of models of mechanical systems. In: Procedia Engineering. Elsevier Ltd, 1230–1235.