In this study, structures damage identification method based on changes in the dynamic characteristics
(frequencies) of the structure are examined, stiffness as well as mass matrices of the curved
(in and out-of-plane vibration) beam elements is formulated using Hamilton's principle. Each node
of both of them possesses seven degrees of freedom including the warping degree of freedom. The
curved beam element had been derived based on the Kang and Yoo’s thin-walled curved beam theory
in 1994. A computer program was developing to carry out free vibration analyses of the curved
beam as well as straight beam. Comparing with the frequencies for other researchers using the general
purpose program MATLAB. Fuzzy logic system (FLS) applied in two stages to calculate the
damage extent and location in simply in and out-of- plane curved beam, the damage deduce by reduction
in stiffness for three levels (20%, 40%, 60%). At the first stage the output faults of the fuzzy system represented by four levels of damage in curved beam (undamaged, slight, moderate, and severe), and at second stage indicate damage location at element with two defuzzification methods (centroid and middle of maximum). The results show that the frequency difference method is efficient to indicate and quantify
damage with accuracy about (99.5%) for slight and moderate damage about (100%) for severe damage. Consequently fuzzy logic performs well for detecting, locating and quantifying damage in curved beam.