Investigation of Cubic Stiffness Non-Linearity for a Bolted Joint

Practically every structure that is used in engineering designs and applications is made up of substructures and a number of components that are connected to one another through a wide variety of independent linkages. Moreover, the increased flexibility within the joint structural system significantly influences the dynamic characteristics of these joints. In order to get accurate simulations and assessments of dynamical responses, it is important to include cubic stiffness non-linearity as a nonlinear joint parameter. Non-linear identification of joint parameter system is the process of creating mathematical models of real structures that are accurate and take into account the non-linearity factor, which is based on measurements of the responses. The present research work aims to identify the non-linear rotational cubic stiffness non-linearity in a cantilever beam bolted structure. This is done by modeling a cantilever beam with a bolted joint at one end and applying sub-structure synthesis theory for the modeling of parameters, including linear and non-linear factors in two sub-structure classes. The linear factors are calculated at a small level of frequency, whereas the cubic stiffness non-linear rotational factor is determined through responses to frequency measurements. Frequency estimation was done under loading conditions, and non-dimensional natural frequencies were obtained by considering stiffness parameters within the response amplitude, and a non-linear zone was established for joint parameter estimation. Through the joint parameter estimation technique, the cubic stiffness coefficient and non-linear rotational cubic stiffness non-linearity were obtained for different modes, which were compared with the exact value, reflecting an error percentage less than 10%. The outcomes reveal that in spite of errors in computing the natural frequency, the calculation of the cubic stiffness coefficient remains very accurate, demonstrating the model’s robustness.