Bifurcation analysis and damage detection in mechanical structures

Bifurcation and damage are two phenomena prompting any structure to unpredicted failure. Their early detection is crucial to maintaining structural health and integrity. In this work, we investigate two topics in bifurcation and damage detection. Trusses with geometric and loading symmetries have been used in many structures to reduce complexity design. Here, bifurcation analysis has been conducted for a two-bar truss and a shallow arch structure with seven bars. Two program packages Gesa and Ansys based on the finite elements method (FEM) have been used to detect the symmetry breaking bifurcation points. The theoretical examination uncovers that the bifurcation prompts a much lower critical load in the presence of little asymmetry in comparison to the symmetric case. The outcomes of bifurcation detection by using Gesa program in Matlab for fully nonlinear analysis and Ansys commercial program show the two programs give results close to the results acquired from the theoretical analysis. Our study opens the door for the researcher to use the two programs for more complicated structures for bifurcation detection analysis since analytically will be hard to use. As for damage detection, the residual error method has been used. This is a technique that relies on observing the residual error in the equation of motion specified for free vibration analysis so as to reveal any changes in the structural dynamic characteristics. The method has been applied on bar, beam and plate to demonstrate its validity. Several numerical simulations with different damage scenarios are presented to assess the robustness and limitations of the method. The sensitivity of the method to noise has been tested with different noise levels as well. Results obtained with the residual error method are compared with those obtained from the absolute difference mode shape curvature (ADMSC) method. The comparison demonstrates that the residual error method can detect and locate damage in the simulated structures with low level of noise.