New techniques for order reduction and damage detection in structural and rotordynamic systems

The first topic in this research work is the order reduction of nonlinear structural dynamic system models which is performed by utilizing the local equivalent linear stiffness method (LELSM). This method is improved in this research work where the updated LELSM modes are developed and employed in the LELSM modal-based order reduction of nonlinear dynamic systems with isolated nonlinearities. The high degree of similarity between the updated LELSM modes and the proper orthogonal modes (POMs) of these systems has been verified in this work. For the forced nonlinear dynamic systems a new type of Ritz vector (called the Sh-B vector) has been found and utilized to produce enhanced reduced models of such systems. The LELSM-based reduced models of the considered nonlinear forced or unforced dynamic systems have been found to be comparable in accuracy and in the number of modes retained in the reduced model to the POD-based reduced models. Unlike POD, the LELSM method does not require a priori simulation of the system. Furthermore, the LELSM method is applied here for approximating the global equivalent stiffness matrix (GELSM) of dynamic systems with mixed clearance and cubic nonlinearities (i.e., beam with switching crack and damaged boundary). The modes corresponding to the GELSM are found to be highly similar to the POMs while the frequencies of the GELSM are found to be a good approximation of the nonlinear frequencies of the considered systems.;The second topic of this work is the damage detection in rotordynamic systems with open and breathing crack models. The correct time-varying area moments of inertia for the cracked element cross-section during shaft rotation are determined here. Hence, two new breathing functions are identified to represent the actual breathing effect on the cracked element stiffness matrix. The new breathing functions are employed in formulating the linear time-periodic finite element equations of motion which are solved via harmonic balance method. A good agreement is found between the analytical and the experimental results of this approach while these results are also found to have a good agreement with many well-known published results in the literature.