Phd in THEORETICAL AND APPLIED MECHANICS

Thesis title: Linear and nonlinear mechanical joint identification through substructure decoupling

Mechanical joints play a crucial role in the performance and reliability of complex engineering structures. In most cases, joints are the primary source of nonlinearity within the structure due to stick-slip interface phenomena or geometric nonlinearities. The effects of joints on the dynamics of the assembled system must be thoroughly understood for effective structural analysis, health monitoring, and design optimization. For this purpose, several techniques have been defined in the field of linear and nonlinear joint identification, with the aim of developing mathematical models for joints that are able to reproduce their real dynamic behavior. Substructure decoupling is a well-established linear technique that can be used to identify the dynamic behaviour of the joint by removing the dynamics of the connected subsystems from that of the assembled system. It has gained importance due to its ability to identify the joint as a standalone subsystem without physically disconnecting it from the assembly, and for the possibility of using different types of data (numerical, analytical or experimental) to model the connected subsystems and the assembly. For these reasons, substructure decoupling is also gaining attention as a nonlinear joint identification method when the primary source of nonlinearity in the assembly is localized in the joint area. In fact, once the joint is identified, the nonlinear variation of its properties can be easily analyzed without involving the entire model of the structure. The FRF Decoupling Method for Nonlinear Systems (FDM-NS) represents the first step in this direction. It is based on the successive application of linear decoupling procedures, using quasi-linear frequency response functions of the assembly, measured at fixed relative displacement levels of the joint degrees of freedom (DoFs). However, this approach has been limited to applications where the joint is a single nonlinear element whose DoFs can be measured directly. The extension of FDM-NS in the presence of multiple nonlinearities within the joint is hindered by the need for decoupling to have information at the joint interface. In fact, interface modeling is an open challenge in substructure decoupling due to the difficulty of obtaining accurate experimental data in this region, including rotations, and the lack of adequate models that capture its flexible motion. This research addresses the problem of linear and nonlinear joint identification through substructure decoupling in applications where the joint interface with other subsystems is inaccessible for measurements. The main effort in the linear case is to improve an iterative coupling/decoupling joint identification technique, based on the System Equivalent Model Mixing (SEMM) expansion method, which provides information at inaccessible DoFs while accurately capturing interface deformation. This study is motivated by the sensitivity of this technique to error propagation. It is also shown that an inappropriate choice of DoFs used to model the joint can lead to a mathematical model that lacks a correct physical interpretation. A detailed analysis of the sources of ill-conditioning in the procedure is therefore performed and different strategies to limit the error propagation in the solution are proposed. The improvements are verified using both numerical and experimental data on a laboratory structure. Furthermore, this technique is compared with other approaches commonly used in the literature to obtain information at inaccessible interface DoFs, and their advantages and disadvantages are discussed. For the nonlinear case, the use of an appropriate interface modeling during the measurements is proposed, allowing the acquisition of quasi-linear FRFs of the assembled system at fixed displacement levels of the inaccessible joint DoFs. This approach represents the first attempt to extend the use of substructure decoupling for nonlinear joint identification in the presence of multiple nonlinearities within the joint, avoiding the need to measure directly at the joint DoFs. The proposed method is tested using experimental data.