טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDemitry Vilensky
SubjectModel Updating of Flexible Structures Using Partial Modal
Measurements
DepartmentDepartment of Mechanical Engineering
Supervisor Full Professor Halevi Yoram
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

Advanced applications of flexible mechanical system that require high accuracy need the development of a reliable model. An analytical model is obtained by modeling methods such as Finite Element. Parallel to the analytical model, there is the experimental system whose real model is not known exactly. From the experimental results it is possible to extract the frequency response and then the modal parameters, which include the eigenvectors and the natural frequencies of the real model. The experimental results may contain also errors stemming from inaccurate measurements, and contain only part of the modal parameters. The model updating problem is usually defined, in broad terms, as combining the analytical model and the experimental results to achieve a better model. In this research thesis some common update methods are reviewed, analyzed and ways of improvements and extension are presented. In addition, a new approach, based on different formulation, is presented.

A common method of model updating is the Generalized Reference Basis method, which gives a closed form solution that satisfies the experimental data.. The main disadvantage is that the updated process does not account for any dependence of the matrices on the physical properties, cannot incorporate any engineering consideration and does not preserve the connectivity of the system. Another disadvantage is its sensitivity to the error of the experimental results. The Connectivity Constrained method solves the optimization problem with structural constraints that are applied to the stiffness matrix. The method finds the closest matrix, with the correct structure, to the updated matrix that is unstructured

The first extension of existing results that is presented in this thesis is the application of the Connectivity Constrained method to the mass matrix update and simultaneous update. Another new result is the Improved Connectivity Constrained method, which has been developed as a result of an analytical error analysis. This method provides better results in terms of sensitivity to noise.

The new Manifold Distance Minimization method comes to solve a fundamental problem that exists in the methods that are based on the Generalized Reference Basis method, which is the limitation of the updated models that can be derived, using any weighting matrix. In this method a development for the mass matrix and the stiffness matrix update and an algorithm for a simultaneous update are presented.