Nonlinear Perturbation Theory for Structural Dynamic Systems
A novel nonlinear perturbation theory for structural dynamic systems is developed that can provide an exact relationship between the perturbation of structural parameters and the perturbation of modal parameters. A system of governing equations based on the developed theory is further derived, which can be utilized for general applications, such as structural reanalyses, eigendata modification, model updating, and damage identification, suitable for all types of structures including mechanical systems, framed structures, and continua. Neither model reduction nor mode shape expansion is required for modal updating and damage identification because information about incomplete measured modal data can be directly employed. The developed theory successfully avoids adopting a Taylor series expansion procedure and then the derivatives of modal parameters are not required. Computational procedures based on the derived nonlinear governing equations are presented for eigendata modification, model updating, and damage identification. The Jacobi transformation method and the accelerated modal method are introduced to make the proposed techniques particularly suitable for cases with a very large perturbation of structural parameters. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed techniques. The results show that the modified modal parameters can be predicted exactly even for cases with a large modification of structural parameters, and the analytical model can be adjusted correctly using the information about limited modal data available.