Eigenstructure assignment in vibrating systems through active and passive approaches

The dynamic behaviour of a vibrating system depends on its eigenstructure, which consists of the eigenvalues and the eigenvectors. In fact, eigenvalues define natural frequencies, damping and settling time, while eigenvectors define the spatial distribution of vibrations, i.e. the mode shape, and also affect the sensitivity of eigenvalues with respect to the system parameters. Therefore, eigenstructure assignment, which is aimed at modifying the system in such a way that it features the desired set of eigenvalues and eigenvectors, is of fundamental importance in mechanical design. However, similarly to several other inverse problems, eigenstructure assignment is inherently challenging, due to its ill-posed nature. Despite the recent advancements of the state of the art in eigenstructure assignment, in fact, there are still important open issues. The available methods for eigenstructure assignment can be grouped into two classes: passive approaches, which consist in modifying the physical parameters of the system, and active approaches, which consist in employing actuators and sensors to exert suitable control forces as determined by a specified control law. Since both these approaches have advantages and drawbacks, it is important to choose the most appropriate strategy for the application of interest. In the present thesis, in fact, are collected passive, active, and even hybrid methods, in which active and passive techniques are concurrently employed. All the methods proposed in the thesis are aimed at solving open issues that emerged from the literature and which have applicative relevance, as well as theoretical. In contrast to several state-of-the-art methods, in fact, the proposed ones implement strategies that enable to ensure that the computed solutions are meaningful and feasible. Moreover, given that in modern mechanical design large-scale systems are increasingly common, computational issues have become a major concern and thus have been adequately addressed in the thesis. The proposed methods have been developed to be general and broadly applicable. In order to demonstrate the versatility of the methods, in the thesis it is provided an extensive numerical assessment, hence diverse test-cases have been used for validation purposes. In order to evaluate without bias the performances of the proposed methods, it has been chosen to employ well-established benchmarks from the literature. Moreover, selected experimental applications are presented in the thesis, in order to determine the capabilities of the developed methods when critically challenged. Given the focus on these issues, it is expected that the methods here proposed can constitute effective tools to improve the dynamic behaviour of vibrating systems and it is hoped that the present work could contribute to spread the use of eigenstructure assignment in the solution of engineering design problems

Stiffness matrix modification with vibration test data by displacement feedback technique

A no spill-over method is developed which uses measured normal modes and natural frequencies to adjust a structural dynamics model in light of displacement feedback technique. By the method, the required displacement feedback gain matrix is determined, and thus the updated stiffness matrix which satisfies the characteristic equation is found in the Frobenius norm sense and the large number of unmeasured high-order modal data of the original model is preserved. The method directly identifies, without iteration, and the solution of this problem is of a compact expression. The numerical example shows that the modal measured data are better incorporated into the updated model

Modelling structural dynamics for control

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1991.Includes bibliographical references (leaves 127-130).by Etienne Balmés.M.S

Investigation and modelling of tremor reducer with the technology of targeted energy transfer

This thesis presents the study of a two-degree-of-freedom (2 DOF) nonlinear system consisting of two grounded linear oscillators coupled to two separate light weight nonlinear energy sinks of an essentially nonlinear stiffness. In this thesis, Targeted Energy Transfer (TET) and NES concept are introduced. Previous studies and research of Energy pumping and NES are presented. The characters in nonlinear energy pumping have been introduced at the start of the thesis. For the aim to design the application of a tremor reduction assessment device, the knowledge of tremor reduction has also been mentioned. Two main parties have been presented in the research: dynamical theoretic method of nonlinear energy pumping study and experiments of nonlinear vibration reduction model. In this thesis, nonlinear energy sink (NES) has been studied and used as a core attachment for the research. A new theoretic method of nonlinear vibration reduction which with two NESs has been attached to a primary system has been designed and tested with the technology of targeted energy transfer. Series connection and parallel connection structure systems have been designed to run the tests. Genetic algorithm has been used and presented in the thesis for searching the fit components. One more experiment has been tested with the final components. The results have been compared to find out most efficiency structure and components for the theoretic model. A tremor reduction experiment has been designed and presented in the thesis. The experiment is for designing an application for reducing human body tremor. By using the theoretic method earlier, the experiment has been designed and tested with a tremor reduction model. The experiment includes several tests, one single NES attached system and two NESs attached systems with different structures. The results of theoretic models and experiment models have been compared. The discussion has been made in the end. At the end of the thesis, some further work has been considered to designing the device of the tremor reduction