Empirical Model of the Non-Linear Vibration of Cracked Reinforced Concrete Beams

摘要

The use of dynamic or modal test data for the damage detection or structural health monitoring of structures has been studied in detail for many years. A particular problem that has been observed for reinforced concrete structures is that they are weakly non-linear when they are cracked. This non-linearity is believed to be due to the transition from crack open to crack closed during the vibration cycle. In this paper the authors present the results of tests on a series of RC beams during which the nonlinear force displacement relationships were measured for different damage states. These results were then used to obtain the parameters for a hyperbolic tangent model of the stiffness transition from crack open to crack closed. The resulting model was then used to simulate the response of the beams at different damage states and results were found to agree with the observed data. Finally, when comparisons were made between the non-linear fit parameters and the damage level it was seen that the parameter defining the sharpness of the transition was exponentially related to the measured reduction in stiffness.