Direct and inverse problems on free vibration of cracked multiple I-section beam with different boundary conditions

Abstract

This article illustrates an exact approach to investigate natural frequencies and mode shapes of cracked multiple I-section beams with different boundary conditions and presents a damage identification method based on the first-order natural frequency and the corresponding mode shape. First, the local flexibility due to a sectional crack in multiple I-section beams is obtained following the procedures in deriving the equations for rectangular section. Next, according to the local flexibility, the mode shape function of vibration for the multiple I-section beams is determined using the recurrence formulas and fundamental solutions. Then, based on the calculation method of natural frequency and mode shape, the damage identification algorithm for crack locations and sizes is presented using the sensitivity method and the singular value decomposition method. Finally, experimental study on a cantilever beam with single I cross section and finite element method simulation of cracked cantilever beam with double I cross section are conducted to validate the proposed approach. Numerical simulation of direct and inverse problems of multiple I-section beams with different boundary conditions is carried out. The effects of crack location, depth, and other parameters on natural frequencies of cracked beams are also investigated and discussed.