Flexibility-based techniques for damage identification in truss and beam structures

Structural Health Monitoring vibration-based methods are extensively employed to identify damage in civil structures, helping to prevent local failures and subsequent structural collapses. Within this category, flexibility matrix has been widely used for its sensitivity to structural damage and because it can be approximated using the lowest eigenfrequencies and mode shapes. In this research context, we introduce an innovative strategy for identifying damage in truss and beam structures by utilizing the flexibility matrix. In real measurements only a few locations are monitored via sensors/accelerometers, and, consequently, a limited number of modal components is estimated. The primary objective of this thesis is to identify structural damage using a reduced number of mode shapes, estimated through a sparse set of modal components. To achieve this goal, we develop an original two-step procedure applicable to both truss and frame structures. In the first step, we conduct a mode shape expansion using a reduced subset of measured modal components. The remaining known components serve as control ones. For the expansion procedure, we consider multiple expansion operators, assuming for each of them the presence of damage in a different element of the structure and varying the damage extent. Consequently, we generate a dataset of expanded mode shapes, each associated with a specific damage location and extent. Using the Total Modal Assurance Criterion, we select the damage scenario that exhibits the highest correspondence to the known control components. This initial hypothesis of damage undergoes verification in the second step of the procedure. In this second step, identification is carried out using two new damage indices: the Strain Change Index for truss structures, and the Curvature Damage Index for beams. Numerical tests on 2D truss and beam structures are conducted to illustrate the algorithm performance. Additionally, experimental tests are executed on two beam structures, yielding promising results.