Akash Dixit from the George W. Woodruff School of Mechanical Engineering at Georgia Tech has successfully demonstrated the use of the Unified Framework to determine the vibration characteristics of a structure consisting of a discontinuous domain. The same framework can be used to determine the eigenvalues, eigenfunctions, and/or eigenvectors associated with other physical problems involving discontinuous domains such as buckling of columns. It was successfully demonstrated that the Unified Framework that has been used to determine the natural frequencies and modes of a damaged beam can also be used to predict the buckling loads and buckling modes of a damaged Euler-column. The resulting expressions were verified using finite-element models for columns with different end conditions. The average difference between the finite-element method and Euler-column theory calculations for a simply supported case for undamaged columns was 1.18% (absolute value). The average difference between the unified theory and finite-element method calculations for damaged columns was 1.12%. The differences for a clamped-free case were 0.76% and 1.01%, respectively. Thus, the Unified Framework predicts results with a similar level of accuracy as finite-element analysis.
- Applicable to damaged elastic, self-adjoint systems for arbitrary boundary conditions and applies to structures with any damage profile or those having more than one area of damage
- Considers the geometric discontinuity at the damage location and perturbation to modes and natural frequencies
- Incorporates the change in mass due to damage and the "breathing" of the damage during bending
- The Unified Framework predicts results to a good level of accuracy with reference to the finite-element result
This invention has applications in structural health monitoring. It can be used to determine physical quantities, such as buckling loads, divergence speeds, and flutter speeds. associated with structures that are damaged.
Structural health monitoring is the process of implementing a damage detection and characterization strategy or damage diagnosis for engineering structures to predict the remaining life of a structure. It also entails developing damage models to predict the response of a damaged structure. There are existing methods that solve for physical quantities associated with continuous domains; however, a comprehensive method is desirable to solve for physical quantities associated with discontinuous domains.