Damage parameters may be estimated by applying damage to the equation of motion. However, the estimation accuracy is usually low, and time-consuming optimization techniques are required for estimating the damage. The two-step method is a common technique to estimate damage of stiffer structures. In this method, the inverse problem is solved firstly to obtain the initial damage condition, and then the forward problem is solved to obtain the dynamic response of the structure . The effectiveness of this method is limited because it cannot handle complex problems caused by cracks, such as mode coupling effects, in the inverse problem. For this reason, a lot of research has been conducted to identify damage of structures using the response of the models, i.e., the forward problem .
In this research, a simplified, one-degree-of-freedom (1-DOF) model is used to analyze the dynamic characteristics of a bridge bearing a crack. The crack is modeled by a spring-damper system as shown in Fig. 1. The crack in the bridge is assumed to be fixed at point 1 and can be moved as a mass point to point 2. The analytical model is then used to identify the damage in the bridge. The moving load is modeled as a mass point in the bridge. This model is simple and easy to realize. The crack and mass point are approximated by a parabolic shape, and a tuned vibration motor is chosen as the moving load. The dynamic characteristics of the bridge bearing the crack are identified by the moving load, and then, the actual characteristics of the bridge bearing the crack are derived by fitting the results of the identification. The elasticity of the crack is taken into consideration in the model for crack representation. The model is validated by experiment. The experimental system is the same as the one used in the identification. The validation of the developed model is performed for the Sagittal plane.
The rest of the paper is organized as follows. In section 2, the method for the identification of dynamic characteristics of the bridge bearing the crack is described. The experimental setup is described in section 3. The identification results and the validation of the developed model are presented in section 4. Section 5 is a summary. An algebraic form for the analytical model is provided in the appendix.
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