Damage Identification of Functionally Graded Beams using Modal Flexibility Sensitivity-based Damage Index

Over the past decades, numerous damage diagnosis techniques based on modal flexibility have been studied and developed for various types of structures, but rarely for structures made of functionally graded (FG) materials. This paper aims to present the extensive applicability of a modal flexibility sensitivity-based damage index termed as MFBDI for damage identification of FG beams. The formulation of this damage index is based on the closed-form of modal flexibility sensitivity derived from the direct algebraic method. The applicability of the offered damage identification method is numerically demonstrated on a clamped-clamped FG beam and a two-span FG beam under (i) single and multiple damage cases, (ii) noise-polluted measurement data, and (iii) only the information of the first few incomplete modes. The identification results indicate that when the noise level added to the mode shape data is below 10%, the offered method can correctly localize the locations of damaged elements and approximately quantify their damage magnitudes in the FG beams. In addition, the influences of the number of used modes, damage magnitudes, and gradient index values are also investigated in the numerical simulations.