A comparative study of different dynamic condensation techniques applied to multi-damage identification of FGM and FG-CNTRC plates

The dynamic condensation method has been recognized as an effective alternative for structural damage identification using spatially-incomplete modal measurements. However, comparative studies of different dynamic condensation techniques applied to the subject of structural damage identification have been scarcely found, especially for composite structures. In this regard, we conduct a comparative study of six typical dynamic condensation techniques utilized for addressing damage identification problems of composite plates made of functionally graded materials (FGM) and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) materials. Firstly, the six techniques consisting of Guyan’s method, Kidder’s method, Neumann series expansion-based second-order model reduction (NSEMR-II) method, improved reduced system (IRS) method, iterated IRS (IIRS) method, and iterative order reduction (IOR) method are reviewed. Then, their performance for reduced Eigen and optimization-damage identification problems are evaluated by studying two numerical examples of FGM plate and FG-CNTRC plate. For solving the optimization-damage identification problem of plate structures, the article proposes to use a hybrid global–local algorithm, Manta Ray Foraging Optimization—Sequential Quadratic Programming (MRFO-SQP), where the MRFO algorithm is utilized for global exploration and the SQP algorithm is used for the local searching process. The comparative study indicates that the IOR technique is the best dynamic condensation technique and is effective for addressing the structural damage identification problems when comparing with the other five techniques. It is also found that the damage identification approach based on the hybrid MRFO–SQP algorithm combined with the IOR technique can archive the high accuracy and low computational cost for damage localization and quantification.