Nonlinear vibrations of cracked reinforced concrete beams
Although a great deal of work in investigating the possibility of using linear vibration techniques to detect damage in bridges has been carried out over the past 25 years, there are still some major concerns, such as poor sensitivity of modal parameters to damage, requirement of baseline data, need of measuring excitation force as well as environmental effects. Nonlinearity in the vibration characteristics when the structure is damaged further complicates the problem and causes doubts on the feasibility of applying these techniques on actual structures. Understanding of the nonlinear behaviour is therefore crucial. The aim of the work presented herein is to improve the current understanding of the nonlinear vibration characteristics of reinforced concrete beams and to assess its importance to the subject of structural health monitoring of bridges. These non-linear vibration characteristics were studied by conducting harmonic excitation vibration tests on reinforced concrete beams at various damage levels. In order to detect and characterise the nonlinear behaviour, both linear and nonlinear system identification techniques were used. Results indicated that the responses of the tested beams showed marked softening behaviour and that this non-linear vibration behaviour varied with increasing damage. The restoring force surface technique was applied to the test data and results suggested that cracks in reinforced concrete beams never fully closed in the vibration cycle. Existing phenomenological models suggested by other researchers were investigated and compared with the experimental results. The study confirmed that a bilinear crack model would not be sufficient to replicate the observed vibrating cracked reinforced concrete beams' behaviour. Based on these phenomenological models, an empirical model was derived. Using the empirical crack model proposed, the author suggested a means of estimating the ratio of cracked and uncracked stiffness of a vibrating cracked reinforced concrete beam. The author further suggested a possible routine for structural health monitoring for reinforced concrete beam and stressed that it could be extended for more complicated structures, like bridges. To improve understanding of the nonlinearities in the vibration characteristics, a damage mechanics model of cracked reinforced concrete beam was suggested. Based on strain softening behaviour of concrete material under tensile force, the model is capable of including damage in the form of a moment rotation relationship over the cracked region. Results from the vibration analysis of the model were compared with experimental data.