Executive Summary : | Second order systems are crucial in modeling real-life phenomena, such as vibrating structures and finite element models. The state trajectory evolution of these systems can be understood by studying the eigenvalues and eigenvectors of the associated quadratic matrix polynomial. The second order system represents the finite element model obtained by discretizing the nonlinear partial differential equation of a vibrating structure. Two important problems associated with this second order model are the Finite Element Model Updating (FEMU) Problem and the Partial Pole Placement Problem. The FEMU problem involves updating the finite element model with minimal changes to match the measured data with the analytical data. This problem is posed as a Polynomial Inverse Eigenvalue Problem (PIEP). This project considers several variations of the FEMU problem, such as FEMU with no spill over, FEMU with incomplete and partially measure data, and FEMU in the presence of uncertainties in measured data.
The project also proposes computationally efficient methods to solve optimization and numerical linear algebra problems arising from solving these FEMU problems. The partial pole placement problem is a problem where the poles are placed in a stability region with minimal control efforts. The project aims to provide computationally efficient linear algebra-inspired solutions in terms of PIEP to these two important problems for second order systems. |