Structural Health Monitoring of Damaged Beams Using an Improved Variational Vibration Model

Abstract

This paper presents a novel modeling and analysis process that can be used in the structural health monitoring process. A previously developed variational vibration model for structural health monitoring purposes of damaged Euler-Bernoulli beams with geometric variations used the central difference method to model the beam. This formulation had a severe restrictive stability condition, which increased computational cost and could produce unstable results. This research proposes a new method to overcome this drawback by introducing the weighted-average and Du Fort-Frankel method into the damage modeling procedure. In the presented two examples, the stability analyses of the proposed two methods are discussed clearly. They show that the weighted-average method is unconditionally stable, whereas the Du Fort-Frankel method has a relaxed stability condition. Moreover, the uncertainties in machining tolerances are considered in two examples, and a stochastic simulation process (namely, the Monte Carlo simulation) is applied to quantify the corresponding uncertainty effects on the system performance. The results from the validation examples clearly show that the proposed method can induce a significant reduction in the computational cost and can be used in structural health monitoring applications.