A Damage Localization and Severity Quantification Method Based on Eigenvalue Assignment

The dynamic properties of mechanical devices are closely related to their structural stiffness. Naturally, the damage alters the local structure stiffness, which causes the change of the overall structural dynamic properties. Typically, the natural frequency (or eigenvalue), as the inherent attribute of the structure itself, is the most readily estimated modal parameter in the structural dynamic testing with high accuracy, which can be harnessed to estimate the stiffness changes of the structure. In order to accurately identify the damage via natural frequencies, a finite element model updating method based on eigenvalue assignment is proposed in this paper. By comparing and analyzing the changes of eigenvalues before and after structural damage, an eigenvalue assignment method is adopted to determine the possible damage positions of the structure, and then the stiffness changes of the structure are evaluated. Finally, numerical studies of a discrete mass-spring system and a cantilever beam are conducted to verify the feasibility and effectiveness of the proposed model updating method. It is found that the damage location and severity can be accurately determined by the proposed eigenvalue assignment method.