Study On Damage Identification Method Based On The Frequency Change And Element Matrix Perturbation Theory

The vibration-based method is an easy and quick method to damage identification. In the filed , highly effective studies have been done by domestic or overseas scientists, and a good many methods which detect damage through changes in mode shape parameters were advanced, but those methods are difficult in application, because they are grave impacted by measure noise, incompletely measure, model errors and uncertainty prompting etc. In order to practice, a damage identification method based on element matrix perturbation theory was advanced, which accords with presently experimentation condition and test level, and its theory, mathematic models, solving methods and application were studied.The element matrix perturbation theory was developed based on perturbation and structural vibration theory in the paper, then the mathematic models of the model updating and damage identification were established according to the above theory, and their algorithms, the sieve method and optimization method, were advanced through analyzing the characteristics of mathematics models and damages. At last, the effect of identifying damages was proofed-test through engineering applications and benchmark problems.The main achievements and conclusions of this paper are summarized below:1. The concept of damage identification element model was advanced to settle the frequencies' insensitivity to damage, and the damage identification parameter based on the damage identification element was founded.2. The 1^st and 2^nd order perturbation equations for structural eigenvalues and eigenvectors and their calculating formulas for 1^st and 2^nd order perturbation were derived based on perturbation and structural vibration theory, and the mathematic models of the model updating and damage identification were established according to the element matrix perturbation theory.3. 4 optimization algorithms based on the mathematics equations of damage identification were summed up, and the sieve method and the combinable sieve method for damage identification were presented according to characteristics of damage identification. The precision to locate and to quantify for the sieve method is higher than the precision of the optimization algorithms.4. The element matrix perturbation theory was applied to the model updating for...