Explicit expressions of the eigenfrequencies of damaged frames

Abstract. The presence of damage can strongly affect the residual carrying capacity and the dynamic properties of frame structures. The uncertainty in the position and intensity of damage implies the difficulty in adopting for practical purposes deterministic analyses, which rigorously require complicated calculations. In this paper, multi-cracked frames are studied considering the crack positions as deterministic whereas the intensities are uncertain. Explicit, although approximated, formulas of the main modal parameters as a function of the damage intensities are proposed. The latter expressions, which extend a previous study on beam-like structures, are built on the basis of detailed analyses, here computed combining the Dynamic Stiffness Matrix (DSM) approach with an efficient solution employing the distribution theory to treat the presence of cracks, and applying the Wittrick and Williams algorithm. An extremely low number of configurations of the frame is adopted to build the approximated solution is adopted. The proposed explicit formulas, which are duly verified for several meaningful cases, are then applied for the dynamic analysis of multi-cracked frames.