PSI - Issue 71

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

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innovative density probability model which can be very helpful for non-linear parameter identifications of any structural element (Zhao et al., 2021). Robert et al. developed a novel quasi-static approach which was employed to revise a collection of Iwan Joint factors, ensuring that the alterations in frequency and damping observed in the finite element (FE) framework corresponded to those obtained from experiments on a testing beam featuring three joints with bolts. The revised model was subsequently validated for its ability to perfectly capture the impact response of the beam, including the impact of modal coupling (Lacayo and Allen, 2019). Ingole et al. discussed about the consideration of cubic stiffness or polynomial stiffness, the parametric identifications can be modeled through the sub-structure synthesis concept, in which the sub subsystems attribute the evolution of non-linearity (Sanjay and Rajurkar, 2022). Gary et al. discussed that the identification of systems having nonlinear characteristics involves the development of accurate mathematical models that accounts for nonlinear presence with the structural joints. This is done by analyzing the input - output data taken from the actual structure (Kerschen et al., 2006). The goal is to accurately represent real structures by identifying the parameters of nonlinear joint systems and including the nonlinearity observed in the response variables. The study of nonlinear system recognition is a broad and well-regarded field within the discipline of structural mechanics at present, as reviewed by Noel et al. (Noël and Kerschen, 2017). Jalali et al. accurately characterized quadratic variables by utilizing the concept of inversion operations, where the nonlinear component was referred to as a combination of quadratic spring and cubic damping (Jalali et al., 2011). Ingole et al. utilized substructure synthesis method to obtain the spectrum expression for nonlinear component dynamic identification. They employed a curve fitting approach to evaluate the frequency sensitivity in the non-linear domain. This analysis revealed a substantial correlation between the actual and analytical results (Ingole and Chatterjee, 2010). The current research proposes a straightforward identification method that relies solely on the bolted structures frequencies. This research study primarily investigates the process of identifying structural systems when nonlinearity is present. The current study aims to develop a mathematical model that can accurately determine the characteristics of non-linear structural elements. To accomplish this, the technique of sub-structure synthesis is employed, which integrates both linear and non-linear stiffness properties to formulate a comprehensive equation that accurately represents the system's dynamical characteristics. Experimental data were matched with the outcomes of a mathematical model for additional analysis. The obtained frequency equation is subsequently employed in reverse computation to determine the non-linear parameter. The research study confirms the effectiveness of the mathematical framework on the cantilever beam, demonstrating a greater level of precision when compared to experimental findings. This article presents a novel method for identifying joint stiffness. The approach relies on the measurement of natural frequencies, making it highly convenient for actual applications. The FE model and the proposed cantilever beam bolted structure model exhibit strong agreement in their results. The precision of parameter estimate was additionally examined for various ranges of joint variables, revealing the identification of a rigid zone. Numerical experiments confirm the validity of the strategy by recreating experimental observations using data generated through theoretical means. The findings demonstrate an effective concurrence between the computed values and the anticipated results. Additionally, it has been found that the method is immune to measurement mistakes. The paper also includes an experimental determination of cubic stiffness nonlinearity for a genuine test construction. The obtained joint variables were subsequently integrated into the FE model. The FE model, when revised with the combination of parameters, yielded frequency ranges that closely matched the observed frequencies. 2 . Mathematical Modeling Substructure synthesis is a method that allows the calculation of FRF’s of a collective arrangement based on the known sub- system FRF’s. The recognition of the subsystems inside the overall system, which includes two sub systems B and C coupled by twin associated co-ordinates, can be achieved by utilizing the test data (Hussain and Ingole, 2024). For estimation of non-linear parameter joint, a cantilever bolted beam having non-linear stiffness (K 2 *), (K 1 *) are considered as shown in Figures 1(a) and (b). The limit state on a cantilever beam is reproduced using an elastic restraint consisting of a rotational spring and a translational spring; this, configuration is referred to as a two-parameter component type.