Vibration Analysis of Cracked Beams Using Adomian Decomposition Method and Non-Baseline Damage Detection via High-Pass Filters

The Adomian decomposition method (ADM) and high-pass filters are employed in this study to investigate the free vibrations and damage detection of cracked Euler-Bernoulli beams. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the mode shapes can be determined for beams consisting of an arbitrary number of cracks under general boundary conditions in a recursive way. Then, a highpass filter is used to extract the irregularity profile from the corresponding mode shape. The location and size of the cracks in the beam can be determined by the peak value of the irregularity profile. The numerical results for different locations and depths of cracks on the damaged beam under different boundary conditions are presented. The results show that the proposed method is effective and accurate. The experimental work for aluminium cantilever beams with one and two cracks was performed to verify the proposed method. The successful detection of cracks in the beam demonstrates that the proposed method has great potential in crack detection of beam-type structures, as it is simple and does not require the mode shapes of an uncracked beam as a baseline.