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M. H. Talebpour, Y. Goudarzi, A. R. Fathalian,
Volume 12, Issue 4 (8-2022)

In this study, the finite element model updating was simulated by reducing the stiffness of the members. Due to lack of access to the experimental results, the data obtained from an analytical model were used in the proposed structural damage scenarios. The updating parameters for the studied structures were defined as a reduction coefficient applied to the stiffness of the members. Parameter variations were calculated by solving an unconstrained nonlinear optimization problem. The objective function in the optimization problem was proposed based on the Multi-Degree-of-Freedom (MDOF) equations of motion as well as the dynamic characteristics of the studied structure. Only the first natural frequency of the damaged structure was used in the proposed updating process, and only one vibration mode was used in the updating problem and damage identification procedure. In addition, as elimination of high-order terms in the proposed formula introduced errors in the final response, the variations of natural frequency and vibration mode for higher-order terms were included in the free vibration equation of the proposed objective function. The Colliding Bodies Optimization (CBO) algorithm was used to solve the optimization problem. The performance of the proposed method was evaluated using the numerical examples, where different conditions were applied to the studied structures. The results of the present study showed that, the proposed method and formulation were capable of efficiently updating the dynamic parameters of the structure as well as identifying the location and severity of the damage using only the first natural frequency of the structure.

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