Damage Identification Of Functionally Graded Beam Structures Based On The Strain Energy Method

Functionally graded materials (FGMs) are non-uniform composite materials with their continuously varying material property in space. FGMs have been increasingly applied in various fields due to their unique graded feature. Because of the accumulation of damage, many structure in these fields failed, and even sometimes led to catastrophic engineering accident, which may cost lots of lives and property. Therefore, it becomes very important to study the structural damage identification method of FGM structures.Based on the finite element method of Euler-Bernoulli beam theory, the computing platform of the finite element software ABAQUS is used to solve the vibration problem of FGM beam structure with material property continuously varied along thickness direction of the section, and study vibration frequencies and mode shapes before and after damage. The element damage index which detects damage defined by strain energy method is computed by numerical method, in which central difference approach and simpson’s rule are applied for second order derivative and integration respectively. Then, detection and location of damage in such beam structure can be indicated by the proposed element damage index. A normalized damage index is obtained by a series of simulated measurement samples. The normalization of damage index gives negative values for undamaged elements and positive ones for potential damaged locations. The key issue is how to determine whether a element is damaged for the positive normalized damage index. Therefore, the concept of a threshold is introduced. The index takes a value over the threshold for damage detection and under the threshold for undamage case. A study on the influence of measurement errors in modal data, and the probability of damage detection and false alarm is also presented.