Damage Identification Of Functionally Graded Beam Structure Based On Modal Strain Energy Sensitivity

Functionally graded materials (FGM), as a new type of composite material, own many excellent properties, and they have a broad application prospect in civil engineering, aviation and other fields with the further theoretical research and the improvement of production process. Cracking phenomenon happens with the cause of external conditions such as load and temperature during the using of FGM structures. It’s a great deal of threat to people’s life and property safety once the engineering accident occurred, therefore, damage identification timely would prevent the engineering accident from happening to some extent.Firstly, stiffness matrix of FGM Euler-Bernoulli beam and expressions of first-order element modal strain energy sensitivity for un-damped systems based on the previous is derived. Then, the sensitivity matrix of FGM Euler-Bernoulli beam to parameters of gradient index K, elastic modulus Eu,EL and volume weight ρy,ρL are obtained. By defining the sensitivity coefficient, the sensitivity of modal strain energy to the above parameters is discussed with considering the influence of noise and boundary conditions to sensitivity. Furthermore, the damage identification equations of FGM Euler-Bernoulli beam derived based on element modal strain energy sensitivity and Taylor’s formula.The above damage identification equations solved by the process of Tikhonov regularization and L-curve, the damage identification method is validated by simple supported beam and continuous beam numerical analysis with considering the influence of noise and boundary conditions to sensitivity. The result indicates this method can both detect the damage position and the damage degree, and with noise resistance ability as well. Finally, in view of many uncertain problems in practical engineering, on the basis of probability and statistics theory, the characteristic of probability (mean and variance) before and after element damaging obtained by the programs of MATLAB setting the FGM beam as numerical examples. According to the probability of damage existence to judge whether the damage of element happened. Results show that the the probability of damage existence of the damaged elements are 1, while the undamaged elements are 0.05. The influence of noise level, damage degree and boundary condition on the recognition performance are also discussed at the same time.